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

Sarah is a professional cyclist who is training for an upcoming marathon. She practises on a circular track and completes one lap at an average speed of 36 km/hr, taking 10 minutes per lap. Sarah wants to improve her performance and aims to complete each lap in 8 minutes to match the pace required for her upcoming race. By how much should she increase her speed (in km/hr) to achieve this new lap time?

  1. 7.5 km/hr

  2. 8 km/hr

  3. 9 km/hr

  4. 10 km/hr
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Current speed = 36 km/hr. Time = 10 min. Distance per lap = 36 * (10/60) = 6 km. Required speed for 8 min = 6 km / (8/60) hr = 6 * (60/8) = 360/8 = 45 km/hr. Increase = 45 - 36 = 9 km/hr.

Multiple choice

Yash started driving his car from Patiala to Ludhiana at 60 km/hr. He travelled for 2 hours at this speed and then increased his speed to 80 km/hr for the next 3 hours, and he reached Ludhiana. On the journey from Ludhiana to Patiala, he drove at 50 km/hr for 3 hours. Now, he has increased his speed to V km/hr to reach Patiala in 2 and a half hours. Find the value of V.

  1. 82 km/hr

  2. 84 km/hr

  3. 86 km/hr

  4. 88 km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Distance Patiala to Ludhiana = (60 * 2) + (80 * 3) = 120 + 240 = 360 km. Return journey distance = 360 km. First 3 hours at 50 km/hr = 150 km. Remaining distance = 360 - 150 = 210 km. Time remaining = 2.5 hours. Speed V = 210 / 2.5 = 84 km/hr.

Multiple choice

Speed of a boat in still water is 9 kmph, and the speed of stream is 3 km per hour. Find the time taken by the boat to go 7.8 km upstream.

  1. 1 hour 15 minutes

  2. 1 hour 18 minutes

  3. 1 hour 12 minutes

  4. 1 hour 6 minutes

  5. 1 hour 10 minutes
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The upstream speed is the boat speed minus the stream speed, which is 9 - 3 = 6 kmph. Time equals distance divided by speed, so 7.8 / 6 = 1.3 hours. 0.3 hours is 0.3 * 60 = 18 minutes, resulting in 1 hour 18 minutes.

Multiple choice

A car starts to go the west at 30 km/hr and another car starts to go the north at 40 km/hr at time t = 0. The distance between them at any time t (in hours) is given by

  1. 10 t

  2. 40 t

  3. 50 t

  4. 70 t
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The cars move in perpendicular directions (West and North). The distance between them at time t forms the hypotenuse of a right triangle with legs 30t and 40t. Distance = sqrt((30t)^2 + (40t)^2) = sqrt(900t^2 + 1600t^2) = sqrt(2500t^2) = 50t.

Multiple choice

Points A and B are 100 km apart. A car starts from point A and another from point B at the same time. If they travel towards each other, they meet after one hour; but if they travel in the same direction (of the slower one), they meet after five hours. What is the difference in their speeds?

  1. 10 kmph

  2. 25 kmph

  3. 40 kmph

  4. 20 kmph

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

Let speeds be u and v. (u+v) = 100/1 = 100. (u-v) = 100/5 = 20. Adding equations: 2u = 120, u = 60. Then v = 40. Difference = 60 - 40 = 20.

Multiple choice

Directions: Compare the two quantities in A and B. A car covers a certain distance at a speed of 40 kmph, and returns at a speed of 60 kmph. Quantity A Quantity B Average speed of the car for the entire journey 50 kmph

  1. Quantity A is greater than quantity B.

  2. Quantity B is greater than quantity A.

  3. Both quantities are equal.

  4. The relationship between the quantities cannot be determined.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Average speed = (2 * v1 * v2) / (v1 + v2) = (2 * 40 * 60) / (40 + 60) = 4800 / 100 = 48 kmph. Quantity A (48) is less than Quantity B (50).