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All Free Mathematics MCQs with Answers

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1,551 questions · page 66 of 78

1301. At 10 a.m. two trains started traveling toward each other from stations 287 miles apart. They passed each other at 1:30 p.m. the same day. If the average speed of the faster train exceeded the average speed of the slower train by 6 miles per hour, which of the following represents the speed of the faster train, in miles per hour?

  • A. 38
  • B. 40
  • C. 44
  • D. 48

Explanation: The trains travel for 3.5 hours, so their combined speed is 287 miles / 3.5 hours = 82 miles per hour.

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Correct answer: 44

1302. Three towns X, Y, and Z are on a river which flows uniformly. Y is equidistant from X and Z. If a boats man rows from X to Y and back in 10 hours and X to Z in 4 hours, find the ratio of speed of the boats man in still water to the speed of the current.

  • A. 2:5
  • B. 5:3
  • C. 3:5
  • D. 1:2

Explanation: Let each section XY and YZ be d km, and let the still-water and current speeds be u km/h and v km/h.

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Correct answer: 5:3

1303. A and B go cycling in the same direction with speeds of 6 km/hr and 12 km/hr. A car from behind passes them in 9 and 10 seconds respectively. What is the speed of the car?

  • A. 22 km/hr
  • B. 33 km/hr
  • C. 66 km/hr
  • D. 44 km/hr

Explanation: If the car's speed is c km/h and its length is L metres, then its relative speeds are c - 6 and c - 12 km/h.

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Correct answer: 66 km/hr

1304. A car travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. What is the average speed for the first 320 km of the tour?

  • A. 70.24 km/hr
  • B. 74. 24 km/hr
  • C. 71.11 km/hr
  • D. 72.21 km/hr

Explanation: The first 160 km takes 160 km / 64 km/h = 2.5 hours, and the next 160 km takes 160 km / 80 km/h = 2 hours.

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Correct answer: 71.11 km/hr

1305. In a journey of 24 miles, two thirds of the distance was travelled with a speed of 40 mph and the remaining with 60 mph. How much time did the journey take?

  • A. 14.4 minutes
  • B. 20 minutes
  • C. 28.8 minutes
  • D. 32 minutes

Explanation: Two thirds of 24 miles is 16 miles, taking 16/40 hour = 0.4 hour = 24 minutes.

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Correct answer: 32 minutes

1306. A man travels a distance of 2 km by walking at a speed of 6 km/hr. He returns back at a speed of 4 km/hr. What is his average speed?

  • A. 4.5 kmph
  • B. 4.8 kmph
  • C. 5 kmph
  • D. 5.1 kmph

Explanation: The total distance is 2 km + 2 km = 4 km. The total time is 2/6 hour + 2/4 hour = 1/3 hour + 1/2 hour = 5/6 hour, so average speed = 4 km…

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Correct answer: 4.8 kmph

1307. A man rows at a speed of 6 km/hr in still water. If the time taken to row a certain distance upstream is 4 times the time taken to row the same distance downstream, what is the speed of the river?

  • A. 1.8 km/hr
  • B. 3 km/hr
  • C. 3.6 km/hr
  • D. 4 km/hr

Explanation: If the river speed is v km/hr, upstream speed is 6 - v kmph and downstream speed is 6 + v kmph.

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Correct answer: 3.6 km/hr

1308. Two trains 140 metres and 120 metres are running in the same direction with speeds 40 kmph and 60 kmph respectively. In what time will the faster train pass the slower one?

  • A. 0.60 minutes
  • B. 0.36 minutes
  • C. 0.78 minutes
  • D. 0.42 minutes

Explanation: For trains moving in the same direction, relative speed is 60 - 40 = 20 kmph = 20 x 1000/60 = 1000/3 metres per minute.

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Correct answer: 0.78 minutes

1309. Yalmaz can cover a distance of 400 metres in 2 minutes. Rayan can cover 1 km in 300 seconds. Find the ratio of their speeds.

  • A. 2:5
  • B. 4:3
  • C. 1:2
  • D. 1:1

Explanation: Yalmaz's speed is 400 m ÷ 120 s = 10/3 m/s. Rayan's speed is 1000 m ÷ 300 s = 10/3 m/s, so their speed ratio is 1:1.

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Correct answer: 1:1

1310. If the ratio of the speeds of A and B to cover a distance of 200 m is 3:4, then the ratio of the time taken to cover the same distance is________?

  • A. 6:8
  • B. 3:7
  • C. 5:4
  • D. 4:3

Explanation: For the same distance, time is inversely proportional to speed. Thus if the speed ratio A:B is 3:4, the time ratio is 1/3:1/4, which…

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Correct answer: 4:3

1311. A boats man can row in still water at speed of 7 km/hr. It takes 6 hours more to travel the same distance in upstream than in downstream if the speed of the river is 3 km/hr. what is the distance between the two destinations?

  • A. 20 km
  • B. 40 km
  • C. 30 km
  • D. 10 km

Explanation: The upstream speed is 7 - 3 = 4 kmph and the downstream speed is 7 + 3 = 10 kmph.

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Correct answer: 40 km

1312. If Afnan drives at 4/5th of his usual speed to his office, he is 6 minutes late. What is his usual time to reach his office?

  • A. 36
  • B. 24
  • C. 30
  • D. 18

Explanation: At 4/5 of his usual speed, the travel time becomes 5/4 of the usual time.

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Correct answer: 24

1313. Two boys starts from the same place walking at the rate of 5 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 8.5 km apart?

  • A. 17 hr
  • B. 14 hr
  • C. 12 hr
  • D. 19 hr

Explanation: Their relative speed is 5.5 kmph - 5 kmph = 0.5 kmph. The time to become 8.5 km apart is 8.5 km ÷ 0.5 kmph = 17 hours.

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Correct answer: 17 hr

1314. A cyclist covers a certain distance in 50 minutes at a speed of 24 kmph. To cover the same distance in 40 minutes, he should travel at a speed of__________?

  • A. 30 kmph
  • B. 27 kmph
  • C. 25 kmph
  • D. 20 kmph

Explanation: The distance covered is 24 kmph x 50/60 hour = 20 km. To cover 20 km in 40/60 hour, the required speed is 20 km ÷ 2/3 hour = 30 kmph.

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Correct answer: 30 kmph

1315. Excluding stoppages, the average speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?

  • A. 9
  • B. 10
  • C. 12
  • D. 20

Explanation: In one hour, the bus covers 45 km including stoppages, while its running speed is 54 kmph.

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Correct answer: 10

1316. If a boat is rowed downstream for 50 km in 5 hours and upstream for 24 km in 6 hours, what is the speed of the boat and the river?

  • A. (7 , 3) km/hr
  • B. (6 , 4) km/hr
  • C. (10 , 4) km/hr
  • D. None of these

Explanation: The downstream speed is 50 km ÷ 5 hours = 10 kmph, and the upstream speed is 24 km ÷ 6 hours = 4 kmph.

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Correct answer: (7 , 3) km/hr

1317. Taimoor left for his school at 6 am by foot and walked at the rate of 2 kmph. After reaching his school he found it was closed and immediately turned back and started walking back to his home at 3 kmph. If he reached his home at 9 am, find the distance between his school and his home.

  • A. 2.5 km
  • B. 7.2 km
  • C. 7 km
  • D. 3.6 km

Explanation: The total walking time is 9 am - 6 am = 3 hours. If the distance is D km, the outward and return times give D/2 hour + D/3 hour = 3 hours…

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Correct answer: 3.6 km

1318. 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. What is the speed of the car?

  • A. 80 kmph
  • B. 102 kmph
  • C. 120 kmph
  • D. 140 kmph

Explanation: Let the car speed be v kmph, so the train speed is 1.5v kmph. Their running-time difference is 75/v hours - 75/(1.5v) hours = 25/v hours…

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Correct answer: 120 kmph

1319. A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 9.30 a.m.?

  • A. 5
  • B. 6
  • C. 7
  • D. 8

Explanation: Moving in opposite directions, their relative rate is 2 rounds/hour + 3 rounds/hour = 5 rounds/hour.

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Correct answer: 7

1320. If a man walks at 6 kmph, he can reach his destination at 9:00 am. However, he walks a little slower and reaches only at 10:00 am. If the distance to his destination was 12 km, at what speed did he walk?

  • A. 5 kmph
  • B. 4 kmph
  • C. 4.5 kmph
  • D. 3 kmph

Explanation: At 6 kmph, the 12 km journey takes 12/6 = 2 hours, so leaving at 7:00 am leads to a 9:00 am arrival.

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Correct answer: 4 kmph
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