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

The distance from the railway station to a village is four kilometres. A boy and a car left the station at the same time for village. Ten minutes later, the boy met the car on its way back from the village. After he had walked another 1/14 km, he met the car once again which drove to the station and was headed back for the village. Find the respective speeds (in km/hr) of the boy and the car, assuming them to be uniform with no stoppages.

  1. 4 km/hr, 50 km/hr

  2. 2.5 km/hr, 40 km/hr

  3. 3 km/hr, 45 km/hr

  4. 3 km/hr, 60 km/hr

  5. 4 km/hr, 45 km/hr
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let v_b be the boy's speed and v_c be the car's speed. The boy walks 4 km. The car travels to the village and back. Using relative speed and time equations for the two meetings, we solve the system of equations. For the first meeting at 10 minutes (1/6 hr), the boy walked 1/6 * v_b and the car traveled 4 + (4 - 1/6 * v_b). Solving these yields 3 km/hr and 45 km/hr.

Multiple choice

Three cars leave A for B in equal time intervals. They reach B simultaneously and then leave for Point C which is 240 km away from B. The first car arrives at C an hour after the second car. The third car, having reached C, immediately turns back and heads towards B. The first and the third car meet a point that is 80 km away from C. What is the difference between the speed of the first and the third car?

  1. 20 kmph

  2. 30 kmph

  3. 50 kmph

  4. 60 kmph
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let speeds be v1, v2, v3. Time intervals are t. They arrive at B at the same time, so they left A at different times. Let v1, v2, v3 be speeds. Distance B to C is 240km. Time difference at C is 1 hour. The meeting point logic and distance equations lead to a speed difference of 60 kmph.

Multiple choice

B starts 4.5 minutes after A from the same point, for a place which is at a distance of 3.5 miles from the starting point. A, on reaching the destination, turns back and walks a mile, where he meets B. If A's speed is a mile in 6 minutes, then B's speed is a mile in ____ minutes.

  1. 8

  2. 10

  3. 12

  4. 9
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A's speed is 1 mile/6 min = 10 mph. B starts 4.5 min late. A travels 3.5 miles, turns back 1 mile, so A travels 4.5 miles total in 4.5 * 6 = 27 minutes. B has been traveling for 27 - 4.5 = 22.5 minutes. B traveled 3.5 - 1 = 2.5 miles. B's speed = 2.5 miles / 22.5 min = 1 mile / 9 minutes.

Multiple choice

Laxman has to cover a distance of 6 km in 45 minutes. If he covers one-half of the distance in two-thirds of the time, what should be his speed to cover the remaining distance in the remaining time?

  1. 12 km/h

  2. 16 km/h

  3. 3 km/h

  4. 8 km/h
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total distance = 6 km, total time = 45 min. First half (3 km) takes 2/3 of 45 min = 30 min. Remaining distance = 3 km, remaining time = 15 min (1/4 hour). Speed = distance / time = 3 / (1/4) = 12 km/h.

Multiple choice

Two cyclists A and B start from the same place at the same time. One goes towards north at 18 km/hr and the other goes towards south at 20 km/hr. How much time will they take to be 95 km apart?

  1. 4 hr and 30 min

  2. 4 hr and 45 min

  3. 5 hr and 16 min

  4. 2 hr and 30 min
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Since they move in opposite directions, their relative speed is 18 + 20 = 38 km/hr. Time = Distance / Speed = 95 / 38 = 2.5 hours, which is 2 hours and 30 minutes.

Multiple choice

Two trains X and Y leave stations A and B, respectively, which are 180 km apart. Train X travels at a speed of 70 km/hr non-stop towards B. Train Y travels at 50 km/hr towards A, but stops for 15 min at a station known to be 60 km away from station B. At what approximate distance (in km) from station A will both the trains meet?

  1. 112

  2. 118

  3. 120

  4. 150

  5. 122
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Train X travels at 70 km/h. Train Y travels at 50 km/h but stops for 15 min (0.25 hours). In 0.25 hours, X covers 70 * 0.25 = 17.5 km. Remaining distance when Y starts moving again is 180 - 17.5 = 162.5 km. Relative speed = 70 + 50 = 120 km/h. Time to meet = 162.5 / 120 = 1.354 hours. Distance from A = 70 * (0.25 + 1.354) = 70 * 1.604 = 112.28 km.

Multiple choice

Three persons A, B and C have to travel from place P to place Q. A's speed is 30 km/hr, whereas the speed of B is 33.33% less than C's speed as well as 11.11% less than average value of speeds of A and C. A starts from point P 2 hrs earlier than B, and C starts from point P y hrs after A. If all three of them reach at the same point after some time, then y is

  1. 4.5

  2. 4

  3. 3.5

  4. None of these

  5. This situation is impossible.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let C's speed be v. B's speed is (2/3)v. Also, B's speed is (8/9) * ((30+v)/2). Solving (2/3)v = (4/9)(30+v) gives 6v = 120 + 4v, so 2v = 120, v = 60 km/hr. B's speed is 40 km/hr. A travels at 30 km/hr. For them to meet at the same point, the time taken by each must align with their start times. Solving the relative time equations yields y = 4.