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 starts walking at 4 kmph and after 4 hours, B starts cycling from the same point as that of A, in the same direction at 10 kmph. After how much distance from the starting point will B catch up with A (correct to two decimal places)?

  1. 24.67 km

  2. 26.67 km

  3. 25.67 km

  4. 23.67 km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Distance A travels in 4 hours = 4 * 4 = 16 km. Relative speed = 10 - 4 = 6 kmph. Time for B to catch A = 16 / 6 = 2.666... hours. Distance from starting point = 10 * 2.666... = 26.67 km.

Multiple choice

Ranjeet drives his car at an average speed of 50 km/hr and reaches his destination in 8 hours. Rahman covers the same distance in 5 hours. If Ranjeet increases his speed by 10 km/hr and Rahman increases his speed by 20 km/hr, then what will be the difference in time taken by them to reach their destination?

  1. 2 hours 30 minutes

  2. 3 hours 40 minutes

  3. 3 hours 20 minutes

  4. 2 hours 40 minutes
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Distance = 50 * 8 = 400 km. Rahman's speed = 400 / 5 = 80 km/hr. New speeds: Ranjeet = 60, Rahman = 100. New times: Ranjeet = 400/60 = 6.66 hr (6 hr 40 min), Rahman = 400/100 = 4 hr. Difference = 2 hr 40 min.

Multiple choice

Train A and train B are running on parallel tracks in the opposite directions with speeds of 36 km/hour and 72 km/hour, respectively. A person is walking in train A in the direction opposite to its motion with a speed of 1.8 km/ hour. Speed (in ms-1) of this person as observed from train B will be close to: (take the distance between the tracks as negligible)

  1. 30.5 ms-1

  2. 29.5 ms-1

  3. 31.5 ms-1

  4. 28.5 ms-1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Train A speed is 10 m/s, Train B speed is 20 m/s. The person in Train A moves at 0.5 m/s opposite to the train, so their ground speed is 10 - 0.5 = 9.5 m/s. Relative to Train B (moving in opposite direction), the speed is 9.5 + 20 = 29.5 m/s.

Multiple choice

Two cars travel the same distance starting at 10:00 am and 11:00 am, respectively, on the same day. They reach their common destination at the same point of time. If the first car travelled for at least 6 hours, then the highest possible value of the percentage by which the speed of the second car could exceed that of the first car is

  1. 10

  2. 20

  3. 30

  4. 25
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let distance be D. Car 1 time = t, speed v1 = D/t. Car 2 time = t-1, speed v2 = D/(t-1). v2/v1 = t/(t-1) = 1 + 1/(t-1). To maximize percentage increase, minimize t. Given t >= 6, min t = 6. v2/v1 = 6/5 = 1.2. Increase is 20%.

Multiple choice

The distance from A to B is 60 km. Partha and Narayan start from A at the same time and move towards B. Partha takes 4 hours more than Narayan to reach B. Moreover, Partha reaches the mid-point of A and B 2 hours before Narayan reaches B. The speed of Partha (in km per hour) is

  1. 3

  2. 4

  3. 5

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

Let Vp and Vn be speeds. 60/Vp = 60/Vn + 4. Also, 30/Vp = 60/Vn - 2. From the second, 60/Vp = 120/Vn - 4. Equating the two expressions for 60/Vp: 60/Vn + 4 = 120/Vn - 4, so 8 = 60/Vn, Vn = 7.5. Then 60/Vp = 60/7.5 + 4 = 8 + 4 = 12, so Vp = 5.

Multiple choice

A motorbike leaves point A at 1 pm and moves towards point B at a uniform speed. A car leaves point B at 2 pm and moves towards point A at a uniform speed which is double that of the motorbike. They meet at 3:40 pm at a point which is 168 km away from A. What is the distance, in km, between A and B?

  1. 364

  2. 378

  3. 380

  4. 388
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Motorbike travels from 1 pm to 3:40 pm (2 hours 40 mins = 8/3 hours). Distance = 168 km. Speed_m = 168 / (8/3) = 63 km/h. Car travels from 2 pm to 3:40 pm (1 hour 40 mins = 5/3 hours). Speed_c = 2 * 63 = 126 km/h. Distance_c = 126 * (5/3) = 210 km. Total distance = 168 + 210 = 378 km.

Multiple choice

The sum of the speeds of boat 'A' and boat 'B', in stillwater is 12 km/hr. The speed of stream is 5 km/hr. If boat'A' takes 24 hours to cover 264 km in downstream, then findthe time taken by boat 'B' to cover 176 km in downstream.

  1. 16 hours

  2. 12 hours

  3. 18 hours

  4. 22 hours

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

Boat A downstream speed = 264 / 24 = 11 km/hr. Downstream speed = Boat speed + Stream speed. 11 = V_A + 5, so V_A = 6 km/hr. Since V_A + V_B = 12, V_B = 6 km/hr. Boat B downstream speed = 6 + 5 = 11 km/hr. Time = 176 / 11 = 16 hours.