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

Ravi starts from his home at 9:00 a.m. and reaches his office at 10:00 a.m. He starts for his home at 5:30 p.m. and walks at a speed increased by 5 km/hr and reaches his home at 6:00 p.m. What is the distance between his home and his office?

  1. 2.5 km

  2. 5 km

  3. 0.5 km

  4. 10 km

  5. 2.14 km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Morning trip: 1 hour. Evening trip: 0.5 hours. Let D be distance and v be speed in morning. v = D/1. Evening speed = v + 5 = D/0.5 = 2D. So D/1 + 5 = 2D, which means D = 5 km.

Multiple choice

Ravi travelled a distance of 60 km at the speed of 15 km/hr, another 40 km at the speed of 10 km/hr and then finally travelled the last 50 km. If his average speed is 15 km/hr, then the speed during 50 km distance is

  1. 20 km/hr

  2. 8.33 km/hr

  3. 12.5 km/hr

  4. 25 km/hr

  5. 16.66 km/hr
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total distance = 60 + 40 + 50 = 150 km. Total time = (60/15) + (40/10) + (50/v) = 4 + 4 + 50/v = 8 + 50/v. Average speed = Total distance / Total time = 150 / (8 + 50/v) = 15. Solving: 150 = 15(8 + 50/v) => 10 = 8 + 50/v => 2 = 50/v => v = 25.

Multiple choice

A car travels a distance of 840 km at a uniform speed. If the speed of the car is increased by 10 km/hr, it takes two hours less to cover the same distance. What is the original speed of the car?

  1. 45 km/hr

  2. 50 km/hr

  3. 60 km/hr

  4. 75 km/hr

  5. 80 km/hr
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let original speed be v. 840/v - 840/(v+10) = 2. 420/v - 420/(v+10) = 1. 420(v+10-v) = v(v+10). 4200 = v^2 + 10v. v^2 + 10v - 4200 = 0. (v+70)(v-60) = 0. Since speed > 0, v = 60.

Multiple choice

The winning relay team in a high school sports competition clocked 48 minutes for a distance of 13.2 km. Its runners A, B, C and D maintained speeds of 15 kmph, 16 kmph, 17 kmph and 18 kmph, respectively. What is the ratio of the time taken by B to that taken by D?

  1. 5 : 16

  2. 5 : 17

  3. 9 : 8

  4. 8 : 9

  5. 9 : 15
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The distance for each runner is not explicitly stated as equal, but in a relay, they cover the total distance. However, the question asks for the ratio of time taken by B and D. Time = Distance / Speed. Since they run the same distance (13.2 km / 4 = 3.3 km each), the ratio of time is (1/16) : (1/18) = 18 : 16 = 9 : 8.

Multiple choice

After travelling a certain distance, a train develops a snag and its speed is decreased to half of its original speed and thus, it reaches its destination 45 minutes late. Had the snag occurred 30 km further, it would have reached its destination 15 minutes earlier. What is the speed of the train?

  1. 90 kmph

  2. 105 kmph

  3. 150 kmph

  4. 120 kmph
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let original speed be v and distance be d. Time taken is d/v. With snag, time is (d1/v) + (d2/(v/2)) = d/v + 45. If snag is 30km further, time is d/v + 30. Solving the system yields v = 120 kmph.

Multiple choice

The speed of a boat in still water is 10 m/s and the speed of the stream is 6 m/s. What is the ratio of the time taken to cover a particular stretch of distance in each direction, if the boat is moving first upstream and back downstream?

  1. 4 : 1

  2. 5 : 4

  3. 2 : 1

  4. 2 : 3

  5. 8 : 1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Upstream speed = 10 - 6 = 4 m/s. Downstream speed = 10 + 6 = 16 m/s. Time is inversely proportional to speed. Ratio of times = 16 : 4 = 4 : 1.

Multiple choice

Two trains start at the same time from station A and station B and proceed towards each other at the speeds of 16 km/hr and 21 km/hr, respectively. When they meet, it is found that one train has travelled 60 km more than the other. What is the distance between the two stations?

  1. 445 km

  2. 444 km

  3. 440 km

  4. 425 km

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

Let t be the time until they meet. Distance A = 16t, Distance B = 21t. Difference is 5t = 60, so t = 12 hours. Total distance = (16+21)*12 = 37*12 = 444 km.

Multiple choice

Two aeroplanes left the airport at same time. First travelled at 22 kmph in the direction of 3500. The second travelled at 29 kmph in the direction of 2200. If both maintains their speed and direction, find the distance between them after 5 hours.

  1. 223.23 km

  2. 228.2 km

  3. 231.58 km

  4. 308.2 km
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The planes travel at 22 kmph and 29 kmph for 5 hours, covering 110 km and 145 km. The angle between 350 degrees and 220 degrees is 130 degrees. Using the law of cosines: d^2 = 110^2 + 145^2 - 2 * 110 * 145 * cos(130). d = sqrt(12100 + 21025 - 31900 * (-0.6427)) = sqrt(33125 + 20502) = sqrt(53627) = 231.575 km.