Quantitative Aptitude

Time, Speed and Distance

2,165 Questions
All Core formulas and unit conversion 441 Boats and streams effective speed 396 Relative speed, meetings, and overtaking 375 Average speed 362 Early and late arrival 321 Proportional relationships 202 Stoppage time per hour 35 Train and stationary or moving object crossing 17 Races and dead heats 16

Time, Speed and Distance Questions

Multiple choice

Two boats are tied at two points, 10 km apart, along a river, one facing upstream and the other facing downstream. The river is flowing at a rate of 3 kmph. The two boats start moving towards each other. The speeds of the boats going downstream and upstream are 12 kmph and 13 kmph, respectively. If they start moving towards each other at the same time, then after how much time will they cross each other?

  1. 12 min

  2. 18 min

  3. 24 min

  4. 28 min

  5. 32 min
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The boats move towards each other. Downstream speed = 12 kmph, Upstream speed = 13 kmph. Relative speed = 12 + 13 = 25 kmph. Time = Distance / Relative Speed = 10 km / 25 kmph = 0.4 hours = 24 minutes.

Multiple choice

A boat can travel a distance of 8.5 km in one hour in still water. If the same boat travels upstream for 72 km and then returns to the starting point, taking 17 hours for the entire journey, then what is the speed of the stream?

  1. 0.5 km/hr

  2. 0.25 km/hr

  3. 0.05 km/hr

  4. 0.025 km/hr

  5. 0.005 km/hr
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let v be stream speed. Boat speed = 8.5. Upstream speed = 8.5-v, downstream = 8.5+v. 72/(8.5-v) + 72/(8.5+v) = 17. 72 * (8.5+v + 8.5-v) / (8.5^2 - v^2) = 17. 72 * 17 / (72.25 - v^2) = 17. 72 = 72.25 - v^2. v^2 = 0.25, v = 0.5.

Multiple choice

A boy running at 10/9th of his actual speed covers 39 km in 2 hours 20 minutes and 24 seconds. Find the actual speed of the boy (approx.).

  1. 15 km/hr

  2. 37 km/hr

  3. 23 km/hr

  4. 150 km/hr

  5. N/A
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Time = 2 hours 20 minutes 24 seconds = 2 + 20/60 + 24/3600 = 2 + 1/3 + 1/150 = (300 + 50 + 1)/150 = 351/150 hours. Speed = Distance / Time = 39 / (351/150) = 39 * 150 / 351 = 150 / 9 = 16.66 km/hr. Since this is 10/9 of actual speed, actual speed = 16.66 * 9/10 = 15 km/hr.

Multiple choice

A fisherman sails his boat along the stream from X to Y, which is 36 km far. Also, it is known that the times taken by him to cover 6 km downstream and 4 km upstream are the same. If the time taken by him to go to point Y and return to point X is 6 hours, then what is the speed of flow of water in the river?

  1. 2.25 km/hr

  2. 2.50 km/hr

  3. 2.75 km/hr

  4. 3.25 km/hr

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let speed of boat be b and stream be s. Downstream speed is b+s, upstream is b-s. 6/(b+s) = 4/(b-s) implies 6b-6s = 4b+4s, so 2b = 10s or b = 5s. Total time for 36 km round trip is 36/(b+s) + 36/(b-s) = 6. Substituting b=5s: 36/(6s) + 36/(4s) = 6, so 6/s + 9/s = 6, 15/s = 6, s = 2.5 km/hr.

Multiple choice

Sanjay wants to reach the railway station at 10:00 am. The station is 10 km away from his house. If Sanjay walks at a speed of 4 km/hr, then at what time should he start from his house in order to reach the station on time?

  1. 10:00 am

  2. 7:30 am

  3. 8:00 am

  4. Cannot be determined

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Time taken = Distance / Speed = 10 km / 4 km/hr = 2.5 hours. 2.5 hours is 2 hours and 30 minutes. To reach at 10:00 am, he must start at 7:30 am.

Multiple choice

Brown starts 2 hours after John and overtakes him in 4 hours. If the difference between the speeds of John and Brown is 20 kmph, what is the distance travelled by Brown before meeting John?

  1. 60 km

  2. 160 km

  3. 240 km

  4. 320 km

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let John's speed be v. Brown's speed is v + 20. John travels for 4 + 2 = 6 hours. Brown travels for 4 hours. Distance = 6v = 4(v + 20). 6v = 4v + 80. 2v = 80, v = 40. Distance = 6 * 40 = 240 km.

Multiple choice

A boat covers a certain distance downstream. It comes back in 1.5 hours. If the speed of the stream is 4 km/h, then it covers the distance in 1 hour (downstream). What is the speed of the boat in still water?

  1. 18 km/h

  2. 20 km/h

  3. 22 km/h

  4. 24 km/h

  5. 28 km/h
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let boat speed be B and stream speed be 4. Downstream speed is B+4. Distance = (B+4)*1. Upstream speed is B-4. Time taken for return is 1.5 hours, so Distance = (B-4)*1.5. Equating: B+4 = 1.5B - 6, so 0.5B = 10, B = 20 km/h.

Multiple choice

Shops A and B are 1200 m apart. The ratio of the speed of Harish to that of Sunil is 3 : 2. If Harish and Sunil start walking towards each other respectively from stations A and B, and meet for the first time at point C, then what is the distance between point C and station B?

  1. 240 m

  2. 360 m

  3. 480 m

  4. 720 m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Harish and Sunil move towards each other. Ratio of speeds = 3:2. They meet at point C. Distance covered by Harish / Distance covered by Sunil = Ratio of speeds = 3/2. Let distance from A to C be 3x and C to B be 2x. 3x + 2x = 1200, so 5x = 1200, x = 240. Distance between C and B = 2x = 480 m.