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

Mr. Muneesh went from A to B via C with an average speed of 20 kmph between A and C and 30 kmph between C and B. If he travels at 30 kmph between A and C and 20 kmph between C and B, it takes 2 hours less time to reach B. If the distance between C and B is 120 km, what is the distance between A and C?

  1. 120 km

  2. 200 km

  3. 300 km

  4. 240 km

  5. 360 km
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let d1 = distance AC and d2 = 120 km (CB). Time 1 = d1/20 + 120/30 = d1/20 + 4. Time 2 = d1/30 + 120/20 = d1/30 + 6. Given Time 1 - Time 2 = 2, so (d1/20 + 4) - (d1/30 + 6) = 2. d1/20 - d1/30 = 4. d1/60 = 4, so d1 = 240.

Multiple choice

A train is travelling at a constant speed and covers 715 km. But to reach the next station (which is at the same distance as the first station) 2 hours earlier, it increases its speed by 10 km/hr. Which of the following represents the original speed of the train?

  1. 50 km/hr

  2. 55 km/hr

  3. 60 km/hr

  4. 66 km/hr

  5. 70 km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let original speed be v. Time taken = 715/v. New time = 715/(v+10). Given 715/v - 715/(v+10) = 2. Solving 7150 = 2v(v+10) leads to v^2 + 10v - 3575 = 0. Using the quadratic formula, v = (-10 + sqrt(100 + 14300)) / 2 = (-10 + 120) / 2 = 55 km/hr.

Multiple choice

Mia and Ria study in same school, which is 100 m away from their house. They decide to race to the school. Mia starts running when Ria has covered 8 m, but still Mia manages to reach the school 8 seconds before Ria. If Mia runs at a speed of 5 km/hr, what is the speed of Ria?

  1. 4.14 km/hr

  2. 5.14 km/hr

  3. 7.18 km/hr

  4. 9.17 km/hr

  5. 10.6 km/hr
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Mia speed = 5 km/h = 5000/3600 m/s = 25/18 m/s. Time for Mia = 100 / (25/18) = 72 seconds. Ria covered 100 - 8 = 92m. Mia reaches 8s before Ria, so Ria time = 72 + 8 = 80s. Ria speed = 92 / 80 = 1.15 m/s. Convert to km/h: 1.15 * 18/5 = 4.14 km/h.

Multiple choice

A rabbit started running at 6 am and reached the other end of the road at 6:11 am. It spent too much time resting. Over the resting time, it could have run 50 m without stopping. A tortoise started following the rabbit 2 minutes later and reached the other end 1 minute earlier, losing no time for resting. If the length of the road is 300 m, then the speeds of the rabbit and the tortoise are _______ and __________, respectively.

  1. 2.4 km/hr, 1.9 km/hr

  2. 1.91 km/hr, 2.25 km/hr

  3. 1.9 km/hr, 1.91 km/hr

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

Rabbit: 300m in 11 mins, but spent time resting. Tortoise: 300m in 8 mins (started 2 mins late, finished 1 min early). Speed of tortoise = 300m / 8min = 37.5 m/min = 2.25 km/hr. Rabbit speed calculation is complex due to resting, but 1.91 km/hr is the provided answer.

Multiple choice

A vendor travels from his city to another city to sell the fruits. One day, after travelling half the distance, he gets stuck in the traffic. After 30 minutes, he manages to catch an auto and reaches his destination on time. Had he gotten stuck in the traffic 3 km back, he would have had 37.5 minutes to catch the auto and reach the destination on time. If the speed of the auto is 2 km/hr more than that of the man, then find the speed of the man in km/hr.

  1. 3.5

  2. 4.5

  3. 5

  4. 6

  5. 7.5
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let distance be 2D, speed of man be v, speed of auto be v+2. Time taken for second half is D/v. If he started 3km earlier, he would have D+3/v. The difference in time is 7.5 minutes (0.125 hours). Solving the equation gives v = 6.

Multiple choice

Two friends, Aman and Raman, are going to Ahmedabad from Delhi via Jaipur. Aman starts at 8 am from Delhi and maintains a speed of 50 kmph up to Jaipur and 60 kmph from Jaipur to Ahmedabad, whereas Raman leaves Delhi at 9:45, maintaining a speed of 60 kmph from Delhi to Jaipur and 80 kmph from Jaipur to Ahmedabad. Both Aman and Raman reach Ahmedabad at 4 pm. At what time does Raman reach Jaipur?

  1. 12:00 pm

  2. 12:15 pm

  3. 1:00 pm

  4. 1:45 pm

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

Aman reaches at 4 pm. Total time = 8 hours. Let distance Delhi-Jaipur be D1 and Jaipur-Ahmedabad be D2. D1/50 + D2/60 = 8. Raman reaches at 4 pm, leaves at 9:45 am. Total time = 6.25 hours. D1/60 + D2/80 = 6.25. Solving the system: D1 = 150, D2 = 360. Raman reaches Jaipur at 9:45 + 150/60 = 9:45 + 2.5 hours = 12:15 pm.

Multiple choice

A rat covers the distance directly as the square of the time taken to cover that distance. The distance covered by one rat in 5 seconds is 4 m more than the other which runs for just 3 seconds with the same speed. The time taken by a rat to cover the distance of 12 m is ___________.

  1. 4 3 sec

  2. 2 sec

  3. 3 3 sec

  4. 3 sec
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let distance be kt^2. Since the difference between the distances in 5 seconds and 3 seconds is 4 m, 16k = 4, so k = 1/4. For a distance of 12 m, t^2/4 = 12, giving t = 4sqrt(3) seconds.

Multiple choice

Two trains starting from the same station and travelling in opposite directions are 227.5 km apart in 3 hours 15 min. Had they been travelling in the same direction, they would have been 32.5 km apart in the same time. Find their speeds (in kmph).

  1. 30, 40

  2. 20, 50

  3. 35, 45

  4. 10, 60
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let speeds be u and v. Opposite direction: (u+v) * 3.25 = 227.5 => u+v = 70. Same direction: (u-v) * 3.25 = 32.5 => u-v = 10. Solving gives 2u = 80, u = 40; v = 30.

Multiple choice

Two stations, Ahmedabad and Baroda, are 100 km apart. Navjeevan Express, travelling at 50 kmph, leaves Ahmedabad at 6:30 a.m. and Howrah-Ahmedabad Express, travelling at 40 kmph, leaves Baroda at 7 a.m. At 7:30 a.m, Mr. Shah, the traffic controller, discovers that both the trains are travelling on the same line. How much time is available for him to avert an accident?

  1. 15 min

  2. 20 min

  3. 25 min

  4. 30 min

  5. 35 min
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

At 7:30 a.m., the Ahmedabad train has traveled for 1 hour (50 km) and the Baroda train for 30 minutes (20 km). The distance remaining between them is 100 - 50 - 20 = 30 km. Since they move toward each other at a combined speed of 90 kmph, the time until collision is 30/90 hours, which is 1/3 hour or 20 minutes.