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Questions.json
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[
{
"Question": "A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?",
"Options": ["120 metres", "180 metres", "324 metres", "150 metres"],
"Correct Option": "D",
"Explanation": "Speed =60 x5m/sec=50m/sec.183Length of the train = (Speed x Time).Length of the train =50x 9m = 150 m.3",
"Topic": "problems-on-trains"
},
{
"Question": "A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:",
"Options": ["45 km/hr", "50 km/hr", "54 km/hr", "55 km/hr"],
"Correct Option": "B",
"Explanation": "Speed of the train relative to man =125m/sec10=25m/sec.2=25x18km/hr25= 45 km/hr.Let the speed of the train bexkm/hr. Then, relative speed = (x- 5) km/hr.x- 5 = 45x= 50 km/hr.",
"Topic": "problems-on-trains"
},
{
"Question": "The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:",
"Options": ["200 m", "225 m", "245 m", "250 m"],
"Correct Option": "C",
"Explanation": "Speed =45 x5m/sec=25m/sec.182Time = 30 sec.Let the length of bridge bexmetres.Then,130 +x=253022(130 +x) = 750x= 245 m.Video Explanation:https://youtu.be/M_d8WufJWKc",
"Topic": "problems-on-trains"
},
{
"Question": "Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:",
"Options": ["1 : 3", "3 : 2", "3 : 4", "None of these"],
"Correct Option": "B",
"Explanation": "Let the speeds of the two trains bexm/sec andym/sec respectively.Then, length of the first train = 27xmetres,and length of the second train = 17ymetres.27x+ 17y= 23x+y27x+ 17y= 23x+ 23y4x= 6yx=3.y2",
"Topic": "problems-on-trains"
},
{
"Question": "A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?",
"Options": ["120 m", "240 m", "300 m", "None of these"],
"Correct Option": "B",
"Explanation": "Speed =54 x5m/sec = 15 m/sec.18Length of the train = (15 x 20)m = 300 m.Let the length of the platform bexmetres.Then,x+ 300= 1536x+ 300 = 540x= 240 m.",
"Topic": "problems-on-trains"
},
{
"Question": "A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?",
"Options": ["65 sec", "89 sec", "100 sec", "150 sec"],
"Correct Option": "B",
"Explanation": "Speed =240m/sec = 10 m/sec.24Required time =240 + 650sec = 89 sec.10",
"Topic": "problems-on-trains"
},
{
"Question": "Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:",
"Options": ["50 m", "72 m", "80 m", "82 m"],
"Correct Option": "A",
"Explanation": "Let the length of each train bexmetres.Then, distance covered = 2xmetres.Relative speed = (46 - 36) km/hr=10 x5m/sec18=25m/sec92x=253692x= 100x= 50.",
"Topic": "problems-on-trains"
},
{
"Question": "A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?",
"Options": ["40 sec", "42 sec", "45 sec", "48 sec"],
"Correct Option": "A",
"Explanation": "Formula for converting from km/hr to m/s:Xkm/hr =Xx5m/s.18Therefore, Speed =45 x5m/sec=25m/sec.182Total distance to be covered = (360 + 140) m = 500 m.Formula for finding Time=DistanceSpeedRequired time =500 x 2sec= 40 sec.25",
"Topic": "problems-on-trains"
},
{
"Question": "Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:",
"Options": ["36", "45", "48", "49"],
"Correct Option": "C",
"Explanation": "Relative speed = (60+ 90) km/hr=150 x5m/sec18=125m/sec.3Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.Required time =2000 x3sec = 48 sec.125",
"Topic": "problems-on-trains"
},
{
"Question": "A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?",
"Options": ["3.6 sec", "18 sec", "36 sec", "72 sec"],
"Correct Option": "C",
"Explanation": "Speed of train relative to jogger = (45 - 9) km/hr = 36 km/hr.=36 x5m/sec18= 10 m/sec.Distance to be covered = (240 + 120) m = 360 m.Time taken =360sec= 36 sec.10",
"Topic": "problems-on-trains"
},
{
"Question": "Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:",
"Options": ["2 : 3", "4 : 3", "6 : 7", "9 : 16"],
"Correct Option": "B",
"Explanation": "Let us name the trains as A and B. Then,(A's speed) : (B's speed) =b:a=16:9= 4 : 3.",
"Topic": "problems-on-trains"
},
{
"Question": "A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?",
"Options": ["3.6", "7.2", "8.4", "10"],
"Correct Option": "B",
"Explanation": "Speed =600m/sec.5 x 60= 2 m/sec.Converting m/sec to km/hr (seeimportant formulassection)=2 x18km/hr5= 7.2 km/hr.",
"Topic": "time-and-distance"
},
{
"Question": "An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1hours, it must travel at a speed of:",
"Options": ["300 kmph", "360 kmph", "600 kmph", "720 kmph"],
"Correct Option": "D",
"Explanation": "Distance = (240 x 5) = 1200 km.Speed = Distance/TimeSpeed = 1200/(5/3) km/hr. \u00a0 \u00a0 [We can write 1hours as 5/3 hours]Required speed =1200 x3km/hr= 720 km/hr.5",
"Topic": "time-and-distance"
},
{
"Question": "If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:",
"Options": ["50 km", "56 km", "70 km", "80 km"],
"Correct Option": "A",
"Explanation": "Let the actual distance travelled bexkm.Then,x=x+ 20101414x= 10x+ 2004x= 200x= 50 km.",
"Topic": "time-and-distance"
},
{
"Question": "A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:",
"Options": ["100 kmph", "110 kmph", "120 kmph", "130 kmph"],
"Correct Option": "C",
"Explanation": "Let speed of the car bexkmph.Then, speed of the train =150x=3xkmph.100275-75=125x(3/2)x10 x 6075-50=5xx24x=25 x24= 120 kmph.5",
"Topic": "time-and-distance"
},
{
"Question": "Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?",
"Options": ["9", "10", "12", "20"],
"Correct Option": "B",
"Explanation": "Due to stoppages, it covers 9 km less.Time taken to cover 9 km =9x 60min= 10 min.54",
"Topic": "time-and-distance"
},
{
"Question": "In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:",
"Options": ["1 hour", "2 hours", "3 hours", "4 hours"],
"Correct Option": "A",
"Explanation": "Let the duration of the flight bexhours.Then,600-600= 200xx+ (1/2)600-1200= 200x2x+ 1x(2x+ 1) = 32x2+x- 3 = 0(2x+ 3)(x- 1) = 0x= 1 hr. \u00a0 \u00a0 \u00a0[neglecting the -ve value ofx]",
"Topic": "time-and-distance"
},
{
"Question": "A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.",
"Options": ["220 km", "224 km", "230 km", "234 km"],
"Correct Option": "B",
"Explanation": "(1/2)x+(1/2)x= 102124x+x= 20212415x= 168 x 20x=168 x 20= 224 km.15",
"Topic": "time-and-distance"
},
{
"Question": "The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:",
"Options": ["70 km/hr", "75 km/hr", "84 km/hr", "87.5 km/hr"],
"Correct Option": "D",
"Explanation": "Let the speed of two trains be 7xand 8xkm/hr.Then, 8x=400= 1004x=100= 12.58Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.",
"Topic": "time-and-distance"
},
{
"Question": "A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:",
"Options": ["35.55 km/hr", "36 km/hr", "71.11 km/hr", "71 km/hr"],
"Correct Option": "C",
"Explanation": "Total time taken =160+160hrs.=9hrs.64802Average speed =320 x2km/hr= 71.11 km/hr.9",
"Topic": "time-and-distance"
},
{
"Question": "A car travelling withof its actual speed covers 42 km in 1 hr 40 min 48 sec. Find the actual speed of the car.",
"Options": ["176km/hr7", "25 km/hr", "30 km/hr", "35 km/hr"],
"Correct Option": "D",
"Explanation": "Time taken = 1 hr 40 min 48 sec = 1 hr 404min = 151hrs =126hrs.57575Let the actual speed bexkm/hr.Then,5xx126= 42775x=42 x 7 x 75= 35 km/hr.5 x 126",
"Topic": "time-and-distance"
},
{
"Question": "In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:",
"Options": ["5 kmph", "6 kmph", "6.25 kmph", "7.5 kmph"],
"Correct Option": "A",
"Explanation": "Let Abhay's speed bexkm/hr.Then,30-30= 3x2x6x= 30x= 5 km/hr.",
"Topic": "time-and-distance"
},
{
"Question": "Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?",
"Options": ["8 kmph", "11 kmph", "12 kmph", "14 kmph"],
"Correct Option": "C",
"Explanation": "Let the distance travelled byxkm.Then,x-x= 210153x- 2x= 60x= 60 km.Time taken to travel 60 km at 10 km/hr =60hrs= 6 hrs.10So, Robert started 6 hours before 2 P.M.i.e.,at 8 A.M.Required speed =60kmph.= 12 kmph.5",
"Topic": "time-and-distance"
},
{
"Question": "It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:",
"Options": ["2 : 3", "3 : 2", "3 : 4", "4 : 3"],
"Correct Option": "C",
"Explanation": "Let the speed of the train bexkm/hr and that of the car beykm/hr.Then,120+480= 81+4=1....(i)xyxy15And,200+400=251+2=1....(ii)xy3xy24Solving (i) and (ii), we get:x= 60 andy= 80.Ratio of speeds = 60 : 80 = 3 : 4.",
"Topic": "time-and-distance"
},
{
"Question": "A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot @ 4 km/hr and partly on bicycle @ 9 km/hr. The distance travelled on foot is:",
"Options": ["14 km", "15 km", "16 km", "17 km"],
"Correct Option": "C",
"Explanation": "Let the distance travelled on foot bexkm.Then, distance travelled on bicycle = (61 -x) km.So,x+(61 -x)= 9499x+ 4(61 -x) = 9 x 365x= 80x= 16 km.",
"Topic": "time-and-distance"
},
{
"Question": "A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is:",
"Options": ["35", "3623", "3712", "40"],
"Correct Option": "D",
"Explanation": "Let distance =xkm and usual rate =ykmph.Then,x-x=402y(y+ 3) = 9x....(i)yy+ 360And,x-x=40y(y- 2) = 3x....(ii)y-2y60On dividing (i) by (ii), we get:x= 40.",
"Topic": "time-and-distance"
},
{
"Question": "Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30\u00b0 and 45\u00b0 respectively. If the lighthouse is 100 m high, the distance between the two ships is:",
"Options": ["173 m", "200 m", "273 m", "300 m"],
"Correct Option": "C",
"Explanation": "Let AB be the lighthouse and C and D be the positions of the ships.Then, AB = 100 m,ACB = 30\u00b0 andADB = 45\u00b0.AB= tan 30\u00b0 =1AC = AB x3= 1003m.AC3AB= tan 45\u00b0 = 1AD = AB = 100 m.ADCD = (AC + AD)= (1003+ 100) m= 100(3+ 1)= (100 x 2.73) m= 273 m.",
"Topic": "height-and-distance"
},
{
"Question": "A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30\u00b0 with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60\u00b0. What is the distance between the base of the tower and the point P?",
"Options": [
"43units",
"8 units",
"12 units",
"Data inadequate",
"None of these"
],
"Correct Option": "D",
"Explanation": "One of AB, AD and CD must have given.So, the data is inadequate.",
"Topic": "height-and-distance"
},
{
"Question": "The angle of elevation of a ladder leaning against a wall is 60\u00b0 and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:",
"Options": ["2.3 m", "4.6 m", "7.8 m", "9.2 m"],
"Correct Option": "D",
"Explanation": "Let AB be the wall and BC be the ladder.Then,ACB = 60\u00b0 and AC = 4.6 m.AC= cos 60\u00b0 =1BC2BC= 2 x AC= (2 x 4.6) m= 9.2 m.",
"Topic": "height-and-distance"
},
{
"Question": "An observer 1.6 m tall is 203away from a tower. The angle of elevation from his eye to the top of the tower is 30\u00b0. The height of the tower is:",
"Options": ["21.6 m", "23.2 m", "24.72 m", "None of these"],
"Correct Option": "A",
"Explanation": "Let AB be the observer and CD be the tower.Draw BECD.Then, CE = AB = 1.6 m,BE = AC = 203m.DE= tan 30\u00b0 =1BE3DE =203m = 20 m.3CD = CE + DE = (1.6 + 20) m = 21.6 m.",
"Topic": "height-and-distance"
},
{
"Question": "From a point P on a level ground, the angle of elevation of the top tower is 30\u00b0. If the tower is 100 m high, the distance of point P from the foot of the tower is:",
"Options": ["149 m", "156 m", "173 m", "200 m"],
"Correct Option": "C",
"Explanation": "Let AB be the tower.Then,APB = 30\u00b0 and AB = 100 m.AB= tan 30\u00b0 =1AP3AP= (AB x3) m= 1003m= (100 x 1.73) m= 173 m.",
"Topic": "height-and-distance"
},
{
"Question": "The angle of elevation of the sun, when the length of the shadow of a tree3times the height of the tree, is:",
"Options": ["30\u00b0", "45\u00b0", "60\u00b0", "90\u00b0"],
"Correct Option": "A",
"Explanation": "Let AB be the tree and AC be its shadow.LetACB =.Then,AC=3cot=3AB= 30\u00b0.",
"Topic": "height-and-distance"
},
{
"Question": "A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :",
"Options": ["14", "110", "715", "815"],
"Correct Option": "D",
"Explanation": "A's 1 day's work =1;15B's 1 day's work =1;20(A + B)'s 1 day's work =1+1=7.152060(A + B)'s 4 day's work =7x 4=7.6015Therefore, Remaining work =1 -7=8.1515",
"Topic": "time-and-work"
},
{
"Question": "A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:",
"Options": ["91days5", "92days5", "93days5", "10"],
"Correct Option": "C",
"Explanation": "(A + B + C)'s 1 day's work =1,4A's 1 day's work =1,16B's 1 day's work =1.12C's 1 day's work =1-1+1=1-7=5.4161244848So, C alone can do the work in48= 93days.55",
"Topic": "time-and-work"
},
{
"Question": "A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?",
"Options": ["12 days", "15 days", "16 days", "18 days"],
"Correct Option": "B",
"Explanation": "A's 2 day's work =1x 2=1.2010(A + B + C)'s 1 day's work =1+1+1=6=1.2030606010Work done in 3 days =1+1=1.10105Now,1work is done in 3 days.5Whole work will be done in (3 x 5) = 15 days.",
"Topic": "time-and-work"
},
{
"Question": "A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:",
"Options": ["20 days", "221days2", "25 days", "30 days"],
"Correct Option": "B",
"Explanation": "Ratio of times taken by A and B = 1 : 3.The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.If difference of time is 2 days, B takes 3 days.If difference of time is 60 days, B takes3x 60= 90 days.2So, A takes 30 days to do the work.A's 1 day's work =130B's 1 day's work =190(A + B)'s 1 day's work =1+1=4=230909045A and B together can do the work in45= 221days.22",
"Topic": "time-and-work"
},
{
"Question": "A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?",
"Options": ["Rs. 375", "Rs. 400", "Rs. 600", "Rs. 800"],
"Correct Option": "B",
"Explanation": "C's 1 day's work =1-1+1=1-7=1.36832424A's wages : B's wages : C's wages =1:1:1= 4 : 3 : 1.6824C's share (for 3 days) = Rs.3 x1x 3200= Rs. 400.24",
"Topic": "time-and-work"
},
{
"Question": "If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:",
"Options": ["4 days", "5 days", "6 days", "7 days"],
"Correct Option": "A",
"Explanation": "Let 1 man's 1 day's work =xand 1 boy's 1 day's work =y.Then, 6x+ 8y=1and 26x+ 48y=1.102Solving these two equations, we get :x=1andy=1.100200(15 men + 20 boy)'s 1 day's work =15+20=1.100200415 men and 20 boys can do the work in 4 days.",
"Topic": "time-and-work"
},
{
"Question": "A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?",
"Options": ["8 hours", "10 hours", "12 hours", "24 hours"],
"Correct Option": "C",
"Explanation": "A's 1 hour's work =1;4(B + C)'s 1 hour's work =1;3(A + C)'s 1 hour's work =1.2(A + B + C)'s 1 hour's work =1+1=7.4312B's 1 hour's work =7-1=1.12212B alone will take 12 hours to do the work.",
"Topic": "time-and-work"
},
{
"Question": "A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in:",
"Options": ["15 days", "20 days", "25 days", "30 days"],
"Correct Option": "C",
"Explanation": "(A + B)'s 1 day's work =110C's 1 day's work =150(A + B + C)'s 1 day's work =1+1=6=3. .... (i)10505025A's 1 day's work = (B + C)'s 1 day's work .... (ii)From (i) and (ii), we get: 2 x (A's 1 day's work) =325A's 1 day's work =3.50B's 1 day's work1-3=2=1.10505025So, B alone could do the work in 25 days.",
"Topic": "time-and-work"
},
{
"Question": "A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?",
"Options": ["23 days", "37 days", "37", "40 days"],
"Correct Option": "C",
"Explanation": "Whole work is done by A in20 x5= 25 days.4Now,1 -4i.e.,1work is done by A and B in 3 days.55Whole work will be done by A and B in (3 x 5) = 15 days.A's 1 day's work =1, (A + B)'s 1 day's work =1.2515B's 1 day's work =1-1=4=2.152515075So, B alone would do the work in75= 371days.22",
"Topic": "time-and-work"
},
{
"Question": "A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished ?",
"Options": ["11:30 A.M.", "12 noon", "12:30 P.M.", "1:00 P.M."],
"Correct Option": "D",
"Explanation": "(P + Q + R)'s 1 hour's work =1+1+1=37.81012120Work done by P, Q and R in 2 hours =37x 2=37.12060Remaining work =1 -37=23.6060(Q + R)'s 1 hour's work =1+1=11.101260Now,11work is done by Q and R in 1 hour.60So,23work will be done by Q and R in60x23=23hours2 hours.60116011So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.",
"Topic": "time-and-work"
},
{
"Question": "A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :",
"Options": ["4 days", "6 days", "8 days", "12 days"],
"Correct Option": "C",
"Explanation": "(A + B + C)'s 1 day's work =1;6(A + B)'s 1 day's work =1;8(B + C)'s 1 day's work =1.12(A + C)'s 1 day's work=2 x1-1+16812=1-5324=324=1.8So, A and C together will do the work in 8 days.",
"Topic": "time-and-work"
},
{
"Question": "A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in:",
"Options": ["5 days", "6 days", "10 days", "101days2"],
"Correct Option": "C",
"Explanation": "(B + C)'s 1 day's work =1+1=7.91236Work done by B and C in 3 days =7x 3=7.3612Remaining work =1 -7=5.1212Now,1work is done by A in 1 day.24So,5work is done by A in24 x5= 10 days.1212",
"Topic": "time-and-work"
},
{
"Question": "X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?",
"Options": ["131days3", "15 days", "20 days", "26 days"],
"Correct Option": "A",
"Explanation": "Work done by X in 8 days =1x 8=1.405Remaining work =1 -1=4.55Now,4work is done by Y in 16 days.5Whole work will be done by Y in16 x5= 20 days.4X's 1 day's work =1, Y's 1 day's work =1.4020(X + Y)'s 1 day's work =1+1=3.402040Hence, X and Y will together complete the work in40= 131days.33",
"Topic": "time-and-work"
},
{
"Question": "A and B can do a job together in 7 days. A is 1times as efficient as B. The same job can be done by A alone in :",
"Options": ["91days3", "11 days", "121days4", "161days3"],
"Correct Option": "B",
"Explanation": "(A's 1 day's work) : (B's 1 day's work) =7: 1 \u00a0 = \u00a0 7 : 4.4Let A's and B's 1 day's work be 7xand 4xrespectively.Then, 7x+ 4x=111x=1x=1.7777A's 1 day's work =1x 7=1.7711",
"Topic": "time-and-work"
},
{
"Question": "A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?",
"Options": ["30 days", "40 days", "60 days", "70 days"],
"Correct Option": "C",
"Explanation": "Let A's 1 day's work =xand B's 1 day's work =y.Then,x+y=1and 16x+ 44y= 1.30Solving these two equations, we get:x=1andy=16060B's 1 day's work =1.60Hence, B alone shall finish the whole work in 60 days.",
"Topic": "time-and-work"
},
{
"Question": "A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:",
"Options": ["Rs. 650", "Rs. 690", "Rs. 698", "Rs. 700"],
"Correct Option": "C",
"Explanation": "S.I. for 1 year = Rs. (854 - 815) = Rs. 39.S.I. for 3 years = Rs.(39 x 3) = Rs. 117.Principal = Rs. (815 - 117) = Rs. 698.",
"Topic": "simple-interest"
},
{
"Question": "Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?",
"Options": [
"Rs. 6400",
"Rs. 6500",
"Rs. 7200",
"Rs. 7500",
"None of these"
],
"Correct Option": "A",
"Explanation": "Let the sum invested in Scheme A be Rs.xand that in Scheme B be Rs. (13900 -x).Then,xx 14 x 2+(13900 -x) x 11 x 2= 350810010028x- 22x= 350800 - (13900 x 22)6x= 45000x= 7500.So, sum invested in Scheme B = Rs. (13900 - 7500) = Rs. 6400.Video Explanation:https://youtu.be/Xi4kU9y6ppk",
"Topic": "simple-interest"
},
{
"Question": "A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?",
"Options": [
"Rs. 4462.50",
"Rs. 8032.50",
"Rs. 8900",
"Rs. 8925",
"None of these"
],
"Correct Option": "D",
"Explanation": "Principal= Rs.100 x 4016.259 x 5= Rs.40162545= Rs. 8925.",
"Topic": "simple-interest"
},
{
"Question": "How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?",
"Options": ["3.5 years", "4 years", "4.5 years", "5 years"],
"Correct Option": "B",
"Explanation": "Time =100 x 81years= 4 years.450 x 4.5Video Explanation:https://youtu.be/WdBzN0Sj8jc",
"Topic": "simple-interest"
},
{
"Question": "Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?",
"Options": ["3.6", "6", "18", "Cannot be determined", "None of these"],
"Correct Option": "B",
"Explanation": "Let rate = R% and time = R years.Then,1200 x R x R= 43210012R2= 432R2= 36R = 6.Video Explanation:https://youtu.be/TjjI4iRkzT0",
"Topic": "simple-interest"
},
{
"Question": "A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?",
"Options": ["3%", "4%", "5%", "6%", "None of these"],
"Correct Option": "D",
"Explanation": "S.I. = Rs. (15500 - 12500) = Rs. 3000.Rate =100 x 3000%= 6%12500 x 4Video Explanation:https://youtu.be/SIcQu1HOmOk",
"Topic": "simple-interest"
},
{
"Question": "An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:",
"Options": ["10%", "10.25%", "10.5%", "None of these"],
"Correct Option": "B",
"Explanation": "Let the sum be Rs. 100. Then,S.I. for first 6 months = Rs.100 x 10 x 1= Rs. 5100 x 2S.I. for last 6 months = Rs.105 x 10 x 1= Rs. 5.25100 x 2So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs. 110.25Effective rate = (110.25 - 100) = 10.25%",
"Topic": "simple-interest"
},
{
"Question": "A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:",
"Options": ["5%", "7%", "71%8", "10%"],
"Correct Option": "D",
"Explanation": "Let the rate be R% p.a.Then,5000 x R x 2+3000 x R x 4= 2200.100100100R + 120R = 2200R =2200= 10.220Rate = 10%.",
"Topic": "simple-interest"
},
{
"Question": "A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest?",
"Options": ["3.6%", "4.5%", "5%", "6%", "None of these"],
"Correct Option": "E",
"Explanation": "Let the original rate be R%. Then, new rate = (2R)%.Note:Here, original rate is for 1 year(s); the new rate is for only 4 months i.e.year(s).725 x R x 1+362.50 x 2R x 1= 33.50100100 x 3(2175 + 725) R = 33.50 x 100 x 3(2175 + 725) R = 10050(2900)R = 10050R =10050= 3.462900Original rate = 3.46%",
"Topic": "simple-interest"
},
{
"Question": "A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:",
"Options": ["Rs. 2000", "Rs. 10,000", "Rs. 15,000", "Rs. 20,000"],
"Correct Option": "C",
"Explanation": "Principal = Rs.100 x 5400= Rs. 15000.12 x 3",
"Topic": "simple-interest"
},
{
"Question": "A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:",
"Options": ["5%", "8%", "12%", "15%"],
"Correct Option": "C",
"Explanation": "S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205.S.I. for 5 years = Rs.2205x 5= Rs. 36753Principal = Rs. (9800 - 3675) = Rs. 6125.Hence, rate =100 x 3675%= 12%6125 x 5Video Explanation:https://youtu.be/UYwiBCRN39s",
"Topic": "simple-interest"
},
{
"Question": "What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years?",
"Options": [
"1 : 3",
"1 : 4",
"2 : 3",
"Data inadequate",
"None of these"
],
"Correct Option": "C",
"Explanation": "Let the principal be P and rate of interest be R%.Required ratio =P x R x 6100=6PR=6= 2 : 3.P x R x 91009PR9Video Explanation:https://youtu.be/GaaEDwTWc6w",
"Topic": "simple-interest"
},
{
"Question": "A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?",
"Options": [
"Rs. 35",
"Rs. 245",
"Rs. 350",
"Cannot be determined",
"None of these"
],
"Correct Option": "D",
"Explanation": "We need to know the S.I., principal and time to find the rate.Since the principal is not given, so data is inadequate.",
"Topic": "simple-interest"
},
{
"Question": "A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6% p.a for 2 years. Find his gain in the transaction per year.",
"Options": ["Rs. 112.50", "Rs. 125", "Rs. 225", "Rs. 167.50"],
"Correct Option": "A",
"Explanation": "Gain in 2 years= Rs.5000 x25x2-5000 x 4 x 24100100= Rs. (625 - 400)= Rs. 225.Gain in 1 year = Rs.225= Rs. 112.502Video Explanation:https://youtu.be/zBjcwqIcmL4",
"Topic": "simple-interest"
},
{
"Question": "A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1stJanuary and 1stJuly of a year. At the end of the year, the amount he would have gained by way of interest is:",
"Options": ["Rs. 120", "Rs. 121", "Rs. 122", "Rs. 123"],
"Correct Option": "B",
"Explanation": "Amount= Rs.1600 x1 +52+ 1600 x1 +52 x 1002 x 100= Rs.1600 x41x41+ 1600 x41404040= Rs.1600 x4141+ 14040= Rs.1600 x 41 x 8140 x 40= Rs. 3321.C.I. = Rs. (3321 - 3200) = Rs. 121",
"Topic": "compound-interest"
},
{
"Question": "The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is:",
"Options": ["625", "630", "640", "650"],
"Correct Option": "A",
"Explanation": "Let the sum be Rs.x. Then,C.I. =x1 +42-x=676x-x=51x.100625625S.I. =xx 4 x 2=2x.1002551x-2x= 162525x= 625.",
"Topic": "compound-interest"
},
{
"Question": "There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?",
"Options": [
"Rs. 2160",
"Rs. 3120",
"Rs. 3972",
"Rs. 6240",
"None of these"
],
"Correct Option": "C",
"Explanation": "Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.R =100 x 60= 10% p.a.100 x 6Now, P = Rs. 12000. T = 3 years and R = 10% p.a.C.I.= Rs.12000 x1 +103- 1100= Rs.12000 x3311000= 3972.",
"Topic": "compound-interest"
},
{
"Question": "What is the difference between the compound interests on Rs. 5000 for 1years at 4% per annum compounded yearly and half-yearly?",
"Options": ["Rs. 2.04", "Rs. 3.06", "Rs. 4.80", "Rs. 8.30"],
"Correct Option": "A",
"Explanation": "C.I. when interestcompounded yearly= Rs.5000 x1 +4x1 +x 4100100= Rs.5000 x26x512550= Rs. 5304.C.I. when interest iscompounded half-yearly= Rs.5000 x1 +23100= Rs.5000 x51x51x51505050= Rs. 5306.04Difference = Rs. (5306.04 - 5304) = Rs. 2.04",
"Topic": "compound-interest"
},
{
"Question": "The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is:",
"Options": ["2", "212", "3", "4"],
"Correct Option": "A",
"Explanation": "Amount = Rs. (30000 + 4347) = Rs. 34347.Let the time benyears.Then, 300001 +7n= 34347100107n=34347=11449=10721003000010000100n= 2 years.",
"Topic": "compound-interest"
},
{
"Question": "What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12 p.c.p.a.?",
"Options": [
"Rs. 9000.30",
"Rs. 9720",
"Rs. 10123.20",
"Rs. 10483.20",
"None of these"
],
"Correct Option": "C",
"Explanation": "Amount= Rs.25000 x1 +123100= Rs.25000 x28x28x28252525= Rs. 35123.20C.I. = Rs. (35123.20 - 25000) = Rs. 10123.20",
"Topic": "compound-interest"
},
{
"Question": "At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?",
"Options": ["6%", "6.5%", "7%", "7.5%"],
"Correct Option": "A",
"Explanation": "Let the rate be R% p.a.Then, 1200 x1 +R2= 1348.321001 +R2=134832=11236100120000100001 +R2=10621001001 +R=106100100R = 6%",
"Topic": "compound-interest"
},
{
"Question": "The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:",
"Options": ["3", "4", "5", "6"],
"Correct Option": "B",
"Explanation": "P1 +20n> 2P6n> 2.1005Now,6x6x6x6> 2.5555So,n= 4 years.",
"Topic": "compound-interest"
},
{
"Question": "Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit?",
"Options": ["Rs. 8600", "Rs. 8620", "Rs. 8820", "None of these"],
"Correct Option": "C",
"Explanation": "Amount= Rs.8000 x1 +52100= Rs.8000 x21x212020= Rs. 8820.",
"Topic": "compound-interest"
},
{
"Question": "The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:",
"Options": ["6.06%", "6.07%", "6.08%", "6.09%"],
"Correct Option": "D",
"Explanation": "Amount of Rs. 100 for 1 yearwhen compounded half-yearly= Rs.100 x1 +32= Rs. 106.09100Effective rate = (106.09 - 100)% = 6.09%",
"Topic": "compound-interest"
},
{
"Question": "Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:",
"Options": ["Rs. 1550", "Rs. 1650", "Rs. 1750", "Rs. 2000"],
"Correct Option": "C",
"Explanation": "C.I.= Rs.4000 x1 +102- 4000100= Rs.4000 x11x11- 40001010= Rs. 840.Sum = Rs.420 x 100= Rs. 1750.3 x 8",
"Topic": "compound-interest"
},
{
"Question": "If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same at the same rate and for the same time?",
"Options": ["Rs. 51.25", "Rs. 52", "Rs. 54.25", "Rs. 60"],
"Correct Option": "A",
"Explanation": "Sum = Rs.50 x 100= Rs. 500.2 x 5Amount= Rs.500 x1 +52100= Rs.500 x21x212020= Rs. 551.25C.I. = Rs. (551.25 - 500) = Rs. 51.25",
"Topic": "compound-interest"
},
{
"Question": "The difference between simple interest and compound on Rs. 1200 for one year at 10% per annum reckoned half-yearly is:",
"Options": ["Rs. 2.50", "Rs. 3", "Rs. 3.75", "Rs. 4", "None of these"],
"Correct Option": "B",
"Explanation": "S.I. = Rs1200 x 10 x 1= Rs. 120.100C.I. = Rs.1200 x1 +52- 1200= Rs. 123.100Difference = Rs. (123 - 120) = Rs. 3.",
"Topic": "compound-interest"
},
{
"Question": "The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?",
"Options": ["8", "10", "12", "Cannot be determined", "None of these"],
"Correct Option": "A",
"Explanation": "15000 x1 +R2- 15000-15000 x R x 2= 96100100150001 +R2- 1 -2R= 9610010015000(100 + R)2- 10000 - (200 x R)= 9610000R2=96 x 2= 643R = 8.Rate = 8%.",
"Topic": "compound-interest"
},
{
"Question": "The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is:",
"Options": ["Rs. 400", "Rs. 500", "Rs. 600", "Rs. 800"],
"Correct Option": "B",
"Explanation": "Let the sum be Rs. P.Then,P1 +102- P= 525100P112- 1= 52510P =525 x 100= 2500.21Sum = Rs . 2500.So, S.I. = Rs.2500 x 5 x 4= Rs. 500100",
"Topic": "compound-interest"
},
{
"Question": "Alfred buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs. 5800, his gain percent is:",
"Options": ["44%7", "55%11", "10%", "12%"],
"Correct Option": "B",
"Explanation": "Cost Price (C.P.) = Rs. (4700 + 800) = Rs. 5500.Selling Price (S.P.) = Rs. 5800.Gain = (S.P.) - (C.P.) = Rs.(5800 - 5500) = Rs. 300.Gain % =300x 100%= 55%550011",
"Topic": "profit-and-loss"
},
{
"Question": "The cost price of 20 articles is the same as the selling price ofxarticles. If the profit is 25%, then the value ofxis:",
"Options": ["15", "16", "18", "25"],
"Correct Option": "B",
"Explanation": "Let C.P. of each article be Re. 1 C.P. ofxarticles = Rs.x.S.P. ofxarticles = Rs. 20.Profit = Rs. (20 -x).20 -xx 100 = 25x2000 - 100x= 25x125x= 2000x= 16.Video Explanation:https://youtu.be/sidqvjUoZxY",
"Topic": "profit-and-loss"
},
{
"Question": "If selling price is doubled, the profit triples. Find the profit percent.",
"Options": ["6623", "100", "10513", "120"],
"Correct Option": "B",
"Explanation": "Let C.P. be Rs.xand S.P. be Rs.y.Then, 3(y-x) = (2y-x)y= 2x.Profit = Rs. (y-x) = Rs. (2x-x) = Rs.x.Profit % =xx 100% = 100%xVideo Explanation:https://youtu.be/dPzF10mGsWE",
"Topic": "profit-and-loss"
},
{
"Question": "In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?",
"Options": ["30%", "70%", "100%", "250%"],
"Correct Option": "B",
"Explanation": "Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420.New C.P. = 125% of Rs. 100 = Rs. 125New S.P. = Rs. 420.Profit = Rs. (420 - 125) = Rs. 295.Required percentage =295x 100%=1475% = 70% (approximately).42021Video Explanation:https://youtu.be/bQA8SB8ycbw",
"Topic": "profit-and-loss"
},
{
"Question": "A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?",
"Options": ["3", "4", "5", "6"],
"Correct Option": "C",
"Explanation": "C.P. of 6 toffees = Re. 1S.P. of 6 toffees = 120% of Re. 1 = Rs.65For Rs.6, toffees sold = 6.5For Re. 1, toffees sold =6 x5= 5.6Video Explanation:https://youtu.be/7wKrnZ0LKA8",
"Topic": "profit-and-loss"
},
{
"Question": "The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?",
"Options": ["Rs. 2000", "Rs. 2200", "Rs. 2400", "Data inadequate"],
"Correct Option": "A",
"Explanation": "Let C.P. be Rs.x.Then,1920 -xx 100 =x- 1280x 100xx1920 -x=x- 12802x= 3200x= 1600Required S.P. = 125% of Rs. 1600 = Rs.125x 1600= Rs 2000.100Video Explanation:https://youtu.be/0tTd5TwCspY",
"Topic": "profit-and-loss"
},
{
"Question": "A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?",
"Options": ["Rs. 18.20", "Rs. 70", "Rs. 72", "Rs. 88.25"],
"Correct Option": "C",
"Explanation": "C.P. = Rs.100x 392= Rs.1000x 392= Rs. 320122.51225Profit = Rs. (392 - 320) = Rs. 72.Video Explanation:https://youtu.be/a36nJFgh5yk",
"Topic": "profit-and-loss"
},
{
"Question": "A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?",
"Options": ["Rs. 1090", "Rs. 1160", "Rs. 1190", "Rs. 1202"],
"Correct Option": "C",
"Explanation": "S.P. = 85% of Rs. 1400 = Rs.85x 1400= Rs. 1190100Video Explanation:https://youtu.be/jn0XIafQvAc",
"Topic": "profit-and-loss"
},
{
"Question": "Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?",
"Options": ["3.5", "4.5", "5.6", "6.5"],
"Correct Option": "C",
"Explanation": "Cost Price of 1 toy = Rs.375= Rs. 31.2512Selling Price of 1 toy = Rs. 33So, Gain = Rs. (33 - 31.25) = Rs. 1.75Profit % =1.75x 100%=28% = 5.6%31.255Video Explanation:https://youtu.be/MhswuvDVWzo",
"Topic": "profit-and-loss"
},
{
"Question": "Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent is:",
"Options": ["30%", "331%3", "35%", "44%"],
"Correct Option": "D",
"Explanation": "Suppose, number of articles bought = L.C.M. of 6 and 5 = 30.C.P. of 30 articles = Rs.5x 30= Rs. 25.6S.P. of 30 articles = Rs.6x 30= Rs. 36.5Gain % =11x 100% = 44%.25",
"Topic": "profit-and-loss"
},
{
"Question": "On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is:",
"Options": ["Rs. 45", "Rs. 50", "Rs. 55", "Rs. 60"],
"Correct Option": "D",
"Explanation": "(C.P. of 17 balls) - (S.P. of 17 balls) = (C.P. of 5 balls)C.P. of 12 balls = S.P. of 17 balls = Rs.720.C.P. of 1 ball = Rs.720= Rs. 60.12",
"Topic": "profit-and-loss"
},
{
"Question": "When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?",
"Options": ["Rs. 21,000", "Rs. 22,500", "Rs. 25,300", "Rs. 25,800"],
"Correct Option": "C",
"Explanation": "85 : 18700 = 115 :xx=18700 x 115= 25300.85Hence, S.P. = Rs. 25,300.",
"Topic": "profit-and-loss"
},
{
"Question": "100 oranges are bought at the rate of Rs. 350 and sold at the rate of Rs. 48 per dozen. The percentage of profit or loss is:",
"Options": ["142% gain7", "15% gain", "142% loss7", "15 % loss"],
"Correct Option": "A",
"Explanation": "C.P. of 1 orange = Rs.350= Rs. 3.50100S.P. of 1 orange = Rs.48= Rs. 412Gain% =0.50x 100%=100% = 142%3.5077",
"Topic": "profit-and-loss"
},
{
"Question": "A shopkeeper sells one transistor for Rs. 840 at a gain of 20% and another for Rs. 960 at a loss of 4%. His total gain or loss percent is:",
"Options": ["515% loss17", "515% gain17", "62% gain3", "None of these"],
"Correct Option": "B",
"Explanation": "C.P. of 1sttransistor = Rs.100x 840= Rs. 700.120C.P. of 2ndtransistor = Rs.100x 960= Rs. 100096So, total C.P. = Rs. (700 + 1000) = Rs. 1700.Total S.P. = Rs. (840 + 960) = Rs. 1800.Gain % =100x 100%= 515%170017",
"Topic": "profit-and-loss"
},
{
"Question": "A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:",
"Options": ["No profit, no loss", "5%", "8%", "10%", "None of these"],
"Correct Option": "B",
"Explanation": "C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.Gain =80x 100% = 5%.1600",
"Topic": "profit-and-loss"
},
{
"Question": "A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Rs. 855, the total profit is:",
"Options": ["Rs. 1425", "Rs. 1500", "Rs. 1537.50", "Rs. 1576"],
"Correct Option": "B",
"Explanation": "Let the total profit be Rs. 100.After paying to charity, A's share = Rs.95 x3= Rs. 57.5If A's share is Rs. 57, total profit = Rs. 100.If A's share Rs. 855, total profit =100x 855= 1500.57",
"Topic": "partnership"
},
{
"Question": "A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit.",
"Options": ["Rs. 1900", "Rs. 2660", "Rs. 2800", "Rs. 2840"],
"Correct Option": "B",
"Explanation": "For managing, A received = 5% of Rs. 7400 = Rs. 370.Balance = Rs. (7400 - 370) = Rs. 7030.Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3)= 39000 : 42000 : 30000= 13 : 14 : 10B's share = Rs.7030 x14= Rs. 2660.37",
"Topic": "partnership"
},
{
"Question": "A, B and C enter into a partnership in the ratio::. After 4 months, A increases his share 50%. If the total profit at the end of one year be Rs. 21,600, then B's share in the profit is:",
"Options": ["Rs. 2100", "Rs. 2400", "Rs. 3600", "Rs. 4000"],
"Correct Option": "D",
"Explanation": "Ratio of initial investments =7:4:6= 105 : 40 : 36.235Let the initial investments be 105x, 40xand 36x.A : B : C =105xx 4 +150x 105xx 8: (40xx 12) : (36xx 12)100= 1680x: 480x: 432x= 35 : 10 : 9.Hence, B's share = Rs.21600 x10= Rs. 4000.54",
"Topic": "partnership"
},
{
"Question": "A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives:",
"Options": ["Rs. 8400", "Rs. 11,900", "Rs. 13,600", "Rs. 14,700"],
"Correct Option": "D",
"Explanation": "Let C =x.Then, B =x+ 5000 and A =x+ 5000 + 4000 =x+ 9000.So,x+x+ 5000 +x+ 9000 = 500003x= 36000x= 12000A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.A's share = Rs.35000 x21= Rs. 14,700.50",
"Topic": "partnership"
},
{
"Question": "Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?",
"Options": [
"5 : 7 : 8",
"20 : 49 : 64",
"38 : 28 : 21",
"None of these"
],
"Correct Option": "B",
"Explanation": "Let their investments be Rs.xfor 14 months, Rs.yfor 8 months and Rs.zfor 7 months respectively.Then, 14x: 8y: 7z= 5 : 7 : 8.Now,14x=598x= 40yy=49x8y720And,14x=5112x= 35zz=112x=16x.7z8355x:y:z=x:49x:16x= 20 : 49 : 64.205",
"Topic": "partnership"
},
{
"Question": "A starts business with Rs. 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital?",
"Options": ["Rs. 7500", "Rs. 8000", "Rs. 8500", "Rs. 9000"],
"Correct Option": "D",
"Explanation": "Let B's capital be Rs.x.Then,3500 x 12=27x314x= 126000x= 9000.",
"Topic": "partnership"
},
{
"Question": "A and B entered into partnership with capitals in the ratio 4 : 5. After 3 months, A withdrewof his capital and B withdrewof his capital. The gain at the end of 10 months was Rs. 760. A's share in this profit is:",
"Options": ["Rs. 330", "Rs. 360", "Rs. 380", "Rs. 430"],
"Correct Option": "A",
"Explanation": "A : B =4xx 3 +4x-1x 4xx 7:5xx 3 +5x-1x 5xx 745= (12x+ 21x) : (15x+ 28x)= 33x:43x= 33 : 43.A's share = Rs.760 x33= Rs. 330.76",
"Topic": "partnership"
},
{
"Question": "A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?",
"Options": ["3 : 5 : 2", "3 : 5 : 5", "6 : 10 : 5", "Data inadequate"],
"Correct Option": "C",
"Explanation": "Let the initial investments of A and B be 3xand 5x.A : B : C = (3xx 12) : (5xx 12) : (5xx 6) = 36 : 60 : 30 = 6 : 10 : 5.",
"Topic": "partnership"
},
{
"Question": "A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?",
"Options": ["Rs. 45", "Rs. 50", "Rs. 55", "Rs. 60"],
"Correct Option": "A",
"Explanation": "A : B : C = (10 x 7) : (12 x 5) : (15 x 3) = 70 : 60 : 45 = 14 : 12 : 9.C's rent = Rs.175 x9= Rs. 45.35",
"Topic": "partnership"
},
{
"Question": "A and B started a business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?",
"Options": ["Rs. 7500", "Rs. 9000", "Rs. 9500", "Rs. 10,000"],
"Correct Option": "A",
"Explanation": "A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.B's share = Rs.25000 x3= Rs. 7,500.10",
"Topic": "partnership"
},
{
"Question": "A began a business with Rs. 85,000. He was joined afterwards by B with Rs. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?",
"Options": ["4 months", "5 months", "6 months", "8 months"],
"Correct Option": "D",
"Explanation": "Suppose B joined forxmonths. Then,Then,85000 x 12=342500 xx1x=85000 x 12= 8.42500 x 3So, B joined for 8 months.",
"Topic": "partnership"
},
{
"Question": "Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs.. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?",
"Options": [
"7 : 6 : 10",
"12 : 15 : 16",
"42 : 45 : 56",
"Cannot be determined"
],
"Correct Option": "B",
"Explanation": "Aman : Rakhi : Sagar = (70,000 x 36) : (1,05,000 x 30) : (1,40,000 x 24) = 12 : 15 : 16.",
"Topic": "partnership"
},
{
"Question": "Arun, Kamal and Vinay invested Rs. 8000, Rs. 4000 and Rs. 8000 respectively in a business. Arun left after six months. If after eight months, there was a gain of Rs. 4005, then what will be the share of Kamal?",
"Options": ["Rs. 890", "Rs. 1335", "Rs. 1602", "Rs. 1780"],
"Correct Option": "A",
"Explanation": "Arun : Kamal : Vinay = (8,000 x 6) : (4,000 x 8) : (8,000 x 8)= 48 : 32 : 64= 3 : 2 : 4.Kamal's share = Rs.4005 x2= Rs. 890.9",
"Topic": "partnership"
},
{
"Question": "Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit?",
"Options": ["Rs. 9,423", "Rs. 10,250", "Rs. 12,500", "Rs. 10,500"],
"Correct Option": "D",
"Explanation": "Simran : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4.Simran's share = Rs.24500 x3= Rs. 10,500.7",
"Topic": "partnership"
},
{
"Question": "A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?",
"Options": ["45%", "455%11", "546%11", "55%"],
"Correct Option": "B",
"Explanation": "Number of runs made by running = 110 - (3 x 4 + 8 x 6)= 110 - (60)= 50.Required percentage =50x 100% = 455%11011Video Explanation:https://youtu.be/X2zTnABqEHU",
"Topic": "percentage"
},
{
"Question": "Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:",
"Options": ["39, 30", "41, 32", "42, 33", "43, 34"],
"Correct Option": "C",
"Explanation": "Let their marks be (x+ 9) andx.Then,x+ 9 =56(x+ 9 +x)10025(x+ 9) = 14(2x+ 9)3x= 99x= 33So, their marks are 42 and 33.",
"Topic": "percentage"
},
{
"Question": "A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:",
"Options": ["588 apples", "600 apples", "672 apples", "700 apples"],
"Correct Option": "D",
"Explanation": "Suppose originally he hadxapples.Then, (100 - 40)% ofx= 420.60xx= 420100x=420 x 100= 700.60Video Explanation:https://youtu.be/-Pv25Do3WwY",
"Topic": "percentage"
},
{
"Question": "What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?",
"Options": ["1", "14", "20", "21"],
"Correct Option": "C",
"Explanation": "Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.Number of such number =14Required percentage =14x 100% = 20%.70Video Explanation:https://youtu.be/cBamI6iRNIA",
"Topic": "percentage"
},
{
"Question": "If A =x% ofyand B =y% ofx, then which of the following is true?",
"Options": [
"A is smaller than B.",
"A is greater than B",
"Relationship between A and B cannot be determined.",
"Ifxis smaller thany, then A is greater than B.",
"None of these"
],
"Correct Option": "E",
"Explanation": "x% ofy=xxy=yxx=y% ofx100100A = B.",
"Topic": "percentage"
},
{
"Question": "If 20% ofa=b, thenb% of 20 is the same as:",
"Options": ["4% ofa", "5% ofa", "20% ofa", "None of these"],
"Correct Option": "A",
"Explanation": "20% ofa=b20a=b.100b% of 20 =bx 20=20ax1x 20=4a= 4% ofa.100100100100",
"Topic": "percentage"
},
{
"Question": "In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age isof the number of students of 8 years of age which is 48. What is the total number of students in the school?",
"Options": ["72", "80", "120", "150", "100"],
"Correct Option": "E",
"Explanation": "Let the number of students bex. Then,Number of students above 8 years of age = (100 - 20)% ofx= 80% ofx.80% ofx= 48 +2of 48380x= 80100x= 100.Video Explanation:https://youtu.be/yPfocU6DA2M",
"Topic": "percentage"
},
{
"Question": "Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.",
"Options": ["2 : 3", "1 : 1", "3 : 4", "4 : 3"],
"Correct Option": "D",
"Explanation": "5% of A + 4% of B =2(6% of A + 8% of B)35A +4B=26A +8B10010031001001A +1B=1A +4B202525751-1A =4-1B202575251A =1B10075A=100=4.B753Required ratio = 4 : 3Video Explanation:YouTube Video",
"Topic": "percentage"
},
{
"Question": "A student multiplied a number by3instead of5.53What is the percentage error in the calculation?",
"Options": ["34%", "44%", "54%", "64%"],
"Correct Option": "D",
"Explanation": "Let the number bex.Then, error =5x-3x=16x.3515Error% =16xx3x 100% = 64%.155x",
"Topic": "percentage"
},
{
"Question": "In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:",
"Options": ["2700", "2900", "3000", "3100"],
"Correct Option": "A",
"Explanation": "Number of valid votes = 80% of 7500 = 6000.Valid votes polled by other candidate = 45% of 6000=45x 6000= 2700.100",
"Topic": "percentage"
},
{
"Question": "Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?",
"Options": ["57%", "60%", "65%", "90%"],
"Correct Option": "A",
"Explanation": "Total number of votes polled = (1136 + 7636 + 11628) = 20400.Required percentage =11628x 100% = 57%.20400",
"Topic": "percentage"
},
{
"Question": "Two tailors X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?",
"Options": ["Rs. 200", "Rs. 250", "Rs. 300", "None of these"],
"Correct Option": "B",
"Explanation": "Let the sum paid to Y per week be Rs.z.Then,z+ 120% ofz= 550.z+120z= 55010011z= 5505z=550 x 5= 250.11",
"Topic": "percentage"
},
{
"Question": "Gauri went to the stationers and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?",
"Options": ["Rs. 15", "Rs. 15.70", "Rs. 19.70", "Rs. 20"],
"Correct Option": "C",
"Explanation": "Let the amount taxable purchases be Rs.x.Then, 6% ofx=30100x=30x100= 5.1006Cost of tax free items = Rs. [25 - (5 + 0.30)] = Rs. 19.70",
"Topic": "percentage"
},
{
"Question": "Rajeev buys good worth Rs. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods.",
"Options": ["Rs. 6876.10", "Rs. 6999.20", "Rs. 6654", "Rs. 7000"],
"Correct Option": "A",
"Explanation": "Rebate = 6% of Rs. 6650 = Rs.6x 6650= Rs. 399.100Sales tax = 10% of Rs. (6650 - 399) = Rs.10x 6251= Rs. 625.10100Final amount = Rs. (6251 + 625.10) = Rs. 6876.10Video Explanation:https://youtu.be/XuiggCTh3SU",
"Topic": "percentage"
},
{
"Question": "The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is:",
"Options": ["4.37%", "5%", "6%", "8.75%"],
"Correct Option": "B",
"Explanation": "Increase in 10 years = (262500 - 175000) = 87500.Increase% =87500x 100% = 50%.175000Required average =50% = 5%.10",
"Topic": "percentage"
},
{
"Question": "Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age?",
"Options": ["2 times", "21times2", "23times4", "3 times"],
"Correct Option": "A",
"Explanation": "Let Ronit's present age bexyears. Then, father's present age =(x+ 3x) years = 4xyears.(4x+ 8) =5(x+ 8)28x+ 16 = 5x+ 403x= 24x= 8.Hence, required ratio =(4x+ 16)=48= 2.(x+ 16)24",
"Topic": "problems-on-ages"
},
{
"Question": "The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?",
"Options": ["4 years", "8 years", "10 years", "None of these"],
"Correct Option": "A",
"Explanation": "Let the ages of children bex, (x+ 3), (x+ 6), (x+ 9) and (x+ 12) years.Then,x+ (x+ 3) + (x+ 6) + (x+ 9) + (x+ 12) = 505x= 20x= 4.Age of the youngest child =x= 4 years.",
"Topic": "problems-on-ages"
},
{
"Question": "A father said to his son, \"I was as old as you are at the present at the time of your birth\". If the father's age is 38 years now, the son's age five years back was:",
"Options": ["14 years", "19 years", "33 years", "38 years"],
"Correct Option": "A",
"Explanation": "Let the son's present age bexyears. Then, (38 -x) =x2x= 38.x= 19.Son's age 5 years back (19 - 5) = 14 years.",
"Topic": "problems-on-ages"
},
{
"Question": "A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?",
"Options": ["7", "8", "9", "10", "11"],
"Correct Option": "D",
"Explanation": "Let C's age bexyears. Then, B's age = 2xyears. A's age = (2x+ 2) years.(2x+ 2) + 2x+x= 275x= 25x= 5.Hence, B's age = 2x= 10 years.",
"Topic": "problems-on-ages"
},
{
"Question": "Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?",
"Options": ["24", "27", "40", "Cannot be determined", "None of these"],
"Correct Option": "A",
"Explanation": "Let the present ages of Sameer and Anand be 5xyears and 4xyears respectively.Then,5x+ 3=114x+ 399(5x+ 3) = 11(4x+ 3)45x+ 27 = 44x+ 3345x- 44x= 33 - 27x= 6.Anand's present age = 4x= 24 years.",
"Topic": "problems-on-ages"
},
{
"Question": "A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:",
"Options": ["14 years", "18 years", "20 years", "22 years"],
"Correct Option": "D",
"Explanation": "Let the son's present age bexyears. Then, man's present age = (x+ 24) years.(x+ 24) + 2 = 2(x+ 2)x+ 26 = 2x+ 4x= 22.",
"Topic": "problems-on-ages"
},
{
"Question": "Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?",
"Options": [
"16 years",
"18 years",
"20 years",
"Cannot be determined",
"None of these"
],
"Correct Option": "A",
"Explanation": "Let the ages of Kunal and Sagar 6 years ago be 6xand 5xyears respectively.Then,(6x+ 6) + 4=11(5x+ 6) + 41010(6x+ 10) = 11(5x+ 10)5x= 10x= 2.Sagar's present age = (5x+ 6) = 16 years.",
"Topic": "problems-on-ages"
},
{
"Question": "The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:",
"Options": ["12 years", "14 years", "18 years", "20 years"],
"Correct Option": "D",
"Explanation": "Let the present ages of son and father bexand (60 -x) years respectively.Then, (60 -x) - 6 = 5(x- 6)54 -x= 5x- 306x= 84x= 14.Son's age after 6 years = (x+ 6) = 20 years..",
"Topic": "problems-on-ages"
},
{
"Question": "At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present ?",
"Options": ["12 years", "15 years", "19 and half", "21 years"],
"Correct Option": "B",
"Explanation": "Let the present ages of Arun and Deepak be 4xyears and 3xyears respectively. Then,4x+ 6 = 264x= 20x= 5.Deepak's age = 3x= 15 years.",
"Topic": "problems-on-ages"
},
{
"Question": "Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?",
"Options": [
"16 years",
"18 years",
"28 years",
"24.5 years",
"None of these"
],
"Correct Option": "D",
"Explanation": "Let Rahul's age bexyears.Then, Sachin's age = (x- 7) years.x- 7=7x99x- 63 = 7x2x= 63x= 31.5Hence, Sachin's age =(x- 7) = 24.5 years.",
"Topic": "problems-on-ages"
},
{
"Question": "The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).",
"Options": ["8, 20, 28", "16, 28, 36", "20, 35, 45", "None of these"],
"Correct Option": "B",
"Explanation": "Let their present ages be 4x, 7xand 9xyears respectively.Then, (4x- 8) + (7x- 8) + (9x- 8) = 5620x= 80x= 4.Their present ages are 4x= 16 years, 7x= 28 years and 9x= 36 years respectively.",
"Topic": "problems-on-ages"
},
{
"Question": "Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?",
"Options": ["2 years", "4 years", "6 years", "8 years"],
"Correct Option": "C",
"Explanation": "Mother's age when Ayesha's brother was born = 36 years.Father's age when Ayesha's brother was born = (38 + 4) years = 42 years.Required difference = (42 - 36) years = 6 years.",
"Topic": "problems-on-ages"
},
{
"Question": "A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?",
"Options": ["32 years", "36 years", "40 years", "48 years"],
"Correct Option": "C",
"Explanation": "Let the mother's present age bexyears.Then, the person's present age =2xyears.52x+ 8=1(x+ 8)522(2x+ 40) = 5(x+ 8)x= 40.",