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 train travels from station P to station Q and then returns back to station P with 20% more speed than the speed in the onward journey. The distance between the two stations is 1000 km and the train takes 37 hours to complete the whole journey taking a halt of 2 hours at station Q. What is the speed of the train in the return journey?

  1. 54 km/hr

  2. 62.86 km/h

  3. 52.38 km/hr

  4. 104.76 km/hr

  5. 60 km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total time is 37 hours, minus 2 hours halt = 35 hours travel time. Let v be the onward speed; return speed is 1.2v. Distance is 1000 km each way. Equation: 1000/v + 1000/(1.2v) = 35. Solving for v gives v = 52.38 km/hr. Return speed = 1.2 * 52.38 = 62.86 km/hr.

Multiple choice

Two trains start simultaneously from Kanpur and Agra moving towards each other with speeds of 70 km/hr and 90 km/hr. When they met each other, it was observed that one of them had covered 350 km more than the other. Find the distance between Kanpur and Agra.

  1. 2400 km

  2. 2550 km

  3. 2700 km

  4. 2800 km
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let time be t. Distances are 70t and 90t. 90t - 70t = 350 => 20t = 350 => t = 17.5 hours. Total distance = 70t + 90t = 160t = 160 * 17.5 = 2800 km.

Multiple choice

There was a race between a hare and a tortoise. The length of the race was 600 m. The speeds of hare and tortoise were 24 km/hr and 0.4 km/hr, respectively. But, along the way, the hare felt tired and slept for some time. After some time, he woke up and completed the race with the same speed as before. But, the race ended in a tie. For how long did the hare sleep?

  1. 92.5 min

  2. 88.5 min

  3. 84.5 min

  4. 60.5 min

  5. 45 min
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Hare speed = 24 km/hr = 400 m/min. Tortoise speed = 0.4 km/hr = 400/60 = 6.67 m/min. Tortoise time = 600 / 6.67 = 90 min. Hare running time = 600 / 400 = 1.5 min. Sleep time = 90 - 1.5 = 88.5 min.

Multiple choice

Sumit travels by metro train. He goes at a speed of 15 km/hr and reaches the station 3 minutes late. He increases his speed to 20 km/hr and reaches 2 minutes earlier. What is the distance between his home and the metro station?

  1. 5 km

  2. 6 km

  3. 10 km

  4. 5.25 km

  5. 15 km
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let distance be D. Time at 15 km/hr is D/15, time at 20 km/hr is D/20. The difference in time is 3 minutes late + 2 minutes early = 5 minutes = 5/60 hours. So, D/15 - D/20 = 5/60. (4D - 3D)/60 = 5/60, which gives D = 5 km.

Multiple choice

Ravi and Ajay start simultaneously from the place A for B which is 60 km apart. Ravi's speed is 4 km/hr less than that of Ajay. Ajay after reaching at B, returns and meets Ravi at a place 12 km away from B. Ravi's speed is

  1. 12 km/hr

  2. 10 km/hr

  3. 8 km/hr

  4. 6 km/hr
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let Ajay's speed be v. Ravi's speed is v-4. Ajay travels 60 km to B and then 12 km back, total 72 km. Ravi travels 60-12 = 48 km. Since they start and meet at the same time, 72/v = 48/(v-4). Solving this gives 72(v-4) = 48v, 72v - 288 = 48v, 24v = 288, v = 12. Ravi's speed is 12-4 = 8 km/hr.

Multiple choice

Ravi goes by a boat running upstream and takes 6 hours 54 minutes to reach a place P, while it takes 3 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the current respectively?

  1. 33 : 13

  2. 23 : 13

  3. 13 : 23

  4. 33 : 12

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

Upstream time = 6h 54m = 6.9h. Downstream time = 3h. Let distance be D. Upstream speed (u-v) = D/6.9. Downstream speed (u+v) = D/3. u = (D/3 + D/6.9)/2 = D(1/6 + 1/13.8) = D(2.3+1)/13.8 = 3.3D/13.8. v = (D/3 - D/6.9)/2 = D(2.3-1)/13.8 = 1.3D/13.8. Ratio u:v = 3.3:1.3 = 33:13.

Multiple choice

Runners A, B and C run a race, with runner A finishing 12 metres ahead of runner B and 18 metres ahead of runner C, while runner B finishes 8 metres ahead of runner C. Each runner travels the entire distance at a constant speed. The length of the race is

  1. 36 metres

  2. 48 metres

  3. 60 metres

  4. 72 metres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let L be the race length. A beats B by 12m, so A/L = B/(L-12). A beats C by 18m, so A/L = C/(L-18). B beats C by 8m, so B/L = C/(L-8). Using the ratios, (L-12)/L = (L-18)/(L-8). Solving for L: (L-12)(L-8) = L(L-18) => L^2 - 20L + 96 = L^2 - 18L => 2L = 96 => L = 48.

Multiple choice

A boat covers 4 km upstream and 4 km downstream in 1 hour. The same boat covers 5 km downstream and 3 km upstream in 55 minutes. What is the speed (in km/hr) of the boat in still water?

  1. 6.5

  2. 7.75

  3. 9

  4. 10.5

  5. 11
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let u be upstream speed and d be downstream speed. 4/u + 4/d = 1. 3/u + 5/d = 55/60 = 11/12. Multiply first by 3 and second by 4: 12/u + 12/d = 3; 12/u + 20/d = 44/12 = 11/3. Subtracting: 8/d = 11/3 - 3 = 2/3. d = 12. Then 4/u + 4/12 = 1 -> 4/u = 2/3 -> u = 6. Speed in still water = (12+6)/2 = 9.

Multiple choice

A man can row at a speed of 10 kmph in still water. The stream flows at a rate of 4 kmph. If he takes 8 hours to row a distance A to B and back, then find the total distance he travels.

  1. 67.2 km

  2. 33.6 km

  3. 45 km

  4. 90 km

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

Speed downstream = 10 + 4 = 14 kmph. Speed upstream = 10 - 4 = 6 kmph. Let distance be D. Time = D/14 + D/6 = 8. (3D + 7D) / 42 = 8. 10D = 336. D = 33.6 km. Total distance (A to B and back) = 2 * 33.6 = 67.2 km.