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

In still water, a boat can cover a distance of 10 km at a speed of 5 km/h in a certain time interval, and during the same time interval, it can cover a distance of 8 km while moving upstream in a river. What is the speed of the river (in km/h)?

  1. 3

  2. 1.5

  3. 1

  4. 2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Boat speed in still water (v) = 10 km / time. So time = 10/5 = 2 hours. Upstream speed = distance / time = 8 km / 2 hours = 4 km/h. Upstream speed = v - stream speed (s). 4 = 5 - s, so s = 1 km/h.

Multiple choice

Two goods trains A and B are running on the same track but in opposite directions. A starts from P and B starts from Q towards each other. P and Q are 250 km apart. A travels 20 km/h and the speed of B is half that of A. What will be the distance between the two trains a minute before the collision?

  1. 0.25 km

  2. 0.75 km

  3. 1 km

  4. 0.5 km
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Relative speed = 20 + 10 = 30 km/h. In 1 minute (1/60 hour), the distance covered is 30 * (1/60) = 0.5 km.

Multiple choice

Shruti travels a distance of 224 km in four parts, for a total travel time of 3 hours. Her speeds in these four parts follow an arithmetic progression, and the corresponding time taken to cover these four parts follow another arithmetic progression. If she travels at a speed of 960 meters per minute for 30 minutes to cover the first part, then the distance, in meters, she travels in the fourth part is

  1. 72,000

  2. 80,000

  3. 86,400

  4. 90,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The times taken for the four parts form an arithmetic progression starting at 30 minutes and summing to 180 minutes, which gives the times as 30, 40, 50, and 60 minutes. The speeds also form an arithmetic progression starting at 57.6 km/h. Solving for the common difference using the total distance of 224 km gives the speed in the fourth part as 86.4 km/h, resulting in a distance of 86,400 meters.

Multiple choice

A train covered a certain distance at a uniform speed. If the train would have been 6 km/h faster, it would have taken 4 hrs less than the scheduled time. And, if the train were slower by 6 km/h, it would have taken 6 hrs more than the scheduled time. Find the distance covered by the train.

  1. 180 kms

  2. 360 kms

  3. 720 kms

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

Let distance be D and speed be S. D/S - D/(S+6) = 4 and D/(S-6) - D/S = 6. Solving these equations: D(6)/(S(S+6)) = 4 => 3D = 2S(S+6). D(6)/(S(S-6)) = 6 => D = S(S-6). Substitute D: 3S(S-6) = 2S(S+6) => 3S - 18 = 2S + 12 => S = 30. Then D = 30(30-6) = 30 * 24 = 720.

Multiple choice

During a workday, two drivers leave the same depot. Mike departs at 7:00 a.m. and travels north at a constant speed of 36 miles per hour. Sara leaves the depot at 9:00 a.m. and travels south at a constant speed of 24 miles per hour. At some time after 9:00 a.m., a dispatcher checks the tracker and finds that the total distance traveled by Mike and Sara combined is 252 miles. At what time did the dispatcher check the tracker?

  1. 11:00 a.m.

  2. 12:00 p.m.

  3. 1:00 p.m.

  4. 1:30 p.m.

  5. 2:00 p.m.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let t be the time in hours after 9:00 a.m. Mike has traveled for t+2 hours. Distance = 36(t+2) + 24t = 252. 36t + 72 + 24t = 252 => 60t = 180 => t = 3. 9:00 a.m. + 3 hours = 12:00 p.m.