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

A man rows to a place and back in 12 hours, covering a distance of 45 km. He realises that he can row 5 km downstream in the same time as 3 km against the stream. The velocity of the stream is

  1. 2 km/hr

  2. 1.5 km/hr

  3. 1 km/hr

  4. 4 km/hr
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let u be boat speed, v be stream speed. Downstream = u+v, upstream = u-v. 5/(u+v) = 3/(u-v) => 5u - 5v = 3u + 3v => 2u = 8v => u = 4v. Total time = 45/(u+v) + 45/(u-v) = 12. 45/(5v) + 45/(3v) = 12. 9/v + 15/v = 12. 24/v = 12. v = 2.

Multiple choice

A boat can travel 15 km upstream in 5 hours. Find the time taken by the boat to cover the same distance downstream when the speed of the current is 1/4th the speed of the boat in still water.

  1. 6 hours

  2. 5 hours

  3. 3 hours

  4. 2 hours

  5. 4 hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Upstream speed = 15 km / 5 hours = 3 km/hr. Let boat speed be B and current speed be C. B - C = 3. Given C = 1/4 B, so B - 0.25B = 3, which means 0.75B = 3, so B = 4 km/hr and C = 1 km/hr. Downstream speed = B + C = 4 + 1 = 5 km/hr. Time = 15 km / 5 km/hr = 3 hours.

Multiple choice

A student goes to school on his Honda Activa. If he drives 5 kmph faster, he reaches 30 minutes early. If he drives 3 kmph slower, he reaches 30 minutes late. The distance (in km) is

  1. 15

  2. 20

  3. 25

  4. 30

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let d be distance and v be speed. d/v - d/(v+5) = 0.5 and d/(v-3) - d/v = 0.5. Solving these equations: d/v - d/(v+5) = d/(v-3) - d/v. 2/v = 1/(v-3) + 1/(v+5). Solving for v gives v = 15. Then d = 30.

Multiple choice

A man travels 404 kilometres partly by rail and steamer. He spends 10 hours more on steamer. If the speed of the steamer is 30 km/hr and the speed of rail is 50 km/hr, how much distance did he cover by steamer?

  1. 407 km

  2. 509 km

  3. 610 km

  4. 339 km
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let d1 be distance by rail, d2 by steamer. d1/50 + 10 = d2/30. d1+d2 = 404. d1 = 404-d2. (404-d2)/50 + 10 = d2/30. Multiply by 150: 3(404-d2) + 1500 = 5d2. 1212 - 3d2 + 1500 = 5d2. 2712 = 8d2. d2 = 339.