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 man can row against the current three-fourth of a kilometre in 15 minutes and returns the same distance in 10 minutes. The ratio of his speed to that of the current is

  1. 3 : 5

  2. 5 : 3

  3. 1 : 5

  4. 5 : 1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Speed against current (u-v) = (3/4 km) / (15/60 h) = 3 km/h. Speed with current (u+v) = (3/4 km) / (10/60 h) = 4.5 km/h. Solving u-v=3 and u+v=4.5 gives 2u=7.5 (u=3.75) and 2v=1.5 (v=0.75). Ratio u:v = 3.75:0.75 = 5:1.

Multiple choice

Shalini travels at a speed of 5 km/h for office from home and reaches 5 minutes late. In the return trip, she travels at 6 km/h to reach her home and reaches 7 minutes earlier. What is the distance between her office and home?

  1. 6 km

  2. 9 km

  3. 4 km

  4. 3 km

  5. 2 km
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let distance be D. Time taken at 5 km/h is D/5. Time taken at 6 km/h is D/6. Given (D/5) - (D/6) = (5+7)/60 = 12/60 = 1/5. Solving D/30 = 1/5 gives D = 6 km.

Multiple choice

Two cities A and B are 90 km apart from each other. Mohan started from city A and Sohan started from city B at the same time. If both of them proceed in the same direction, they will meet in 9 hours and if they proceed in opposite directions, they will meet in 9/7 hours. Calculate their speeds (in km/hr).

  1. 10 km/hr and 30 km/hr

  2. 40 km/hr and 10 km/hr

  3. 40 km/hr and 30 km/hr

  4. 90 km/hr and 70 km/hr

  5. 10 km/hr and 90 km/hr
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speeds be u and v. Relative speed in same direction is u - v = 90/9 = 10. Relative speed in opposite direction is u + v = 90/(9/7) = 70. Solving the system u - v = 10 and u + v = 70 gives u = 40 and v = 30.

Multiple choice

Four persons Jem, Sem, Kem and Jesu participated in a race. All the four, i.e. Jem, Sem, Kem and Jesu are running with a uniform speed to get the first, second, third and fourth positions, respectively, in a 40 km race. If Jem beats Sem by 2 km and Sem beats Kem by 4 km, and Kem beats Jesu by 2 km, then by what distance does Jem beat Jesu?

  1. 8.50 km

  2. 7.51 km

  3. 6.50 km

  4. 5.60 km

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

Jem beats Sem by 2 km in 40 km, so Jem:Sem = 40:38. Sem beats Kem by 4 km, so Sem:Kem = 40:36 = 10:9. Kem beats Jesu by 2 km, so Kem:Jesu = 40:38 = 20:19. Ratio Jem/Jesu = (40/38) * (40/36) * (40/38) = (20/19) * (10/9) * (20/19) = 4000 / 3249. Distance = 40 * (1 - 3249/4000) = 40 * (751/4000) = 7.51 km.

Multiple choice

A man jogs along a certain route to a place and walks back from that place to the starting point, following the same route. What is his average speed for the entire activity? Statements: A. His jogging speed is one-and-a-half times his walking speed. B. By walking, he covers a distance of 8 km in 120 min. C. Total distance travelled by him in entire activity is 20 km.

  1. Only A and B together are sufficient.

  2. Only A and C together are sufficient.

  3. Only B and C together are sufficient.

  4. Any two of them together are sufficient.

  5. All three statements are necessary.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Average speed = Total distance / Total time. Statement A gives the ratio of speeds. Statement B gives the walking speed (8km / 2hr = 4km/h). Statement C gives the total distance. To find the average speed, we need the total time, which requires both the walking speed (from B) and the jogging speed (from A). C is redundant if we know the distance is covered in a specific route.

Multiple choice

A truck driver had to deliver goods he was carrying to a port which was 932 km away from the town where he loaded the goods. He drove his truck at an average speed of 42 kmph in cities and for the rest of the journey on the highway, he drove at an average speed of 64 kmph. If he took 18 hours in total to cover the entire distance, then for how long did he travel on the highway?

  1. 7 hours and 12 minutes

  2. 8 hours

  3. 8 hours and 34 minutes

  4. 9 hours

  5. 9 hours and 14 minutes
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let x be highway time. Then (18-x) is city time. 64x + 42(18-x) = 932. 64x + 756 - 42x = 932. 22x = 176. x = 8 hours.

Multiple choice

David has to row his boat 99 km downstream and return the same distance upstream. Speed of the stream is 1 km/hour. If he takes 2 hours less to row the boat downstream than to return upstream, then find the speed of the boat in still water.

  1. 100 km/hour

  2. 80 km/hour

  3. 10 km/hour

  4. 15 km/hour

  5. 20 km/hour
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let boat speed be v. Downstream speed = v + 1. Upstream speed = v - 1. Time difference: 99/(v-1) - 99/(v+1) = 2. 99 * (v+1 - v+1) / (v^2 - 1) = 2. 99 * 2 / (v^2 - 1) = 2. 99 = v^2 - 1. v^2 = 100, v = 10.

Multiple choice

Directions: Study the given information carefully to answer the question that follows: The speeds of Boat A and Boat B are in the ratio 4 : 5. The speed of the current with respect to Boat A is 1/4th and with respect to Boat B is 1/5th. Find the distance covered downstream by Boat B in 1.5 hours and speed of current is 5 km/hr.

  1. 36 km

  2. 40 km

  3. 42 km

  4. 45 km

  5. 48 km
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let speed of A = 4k, B = 5k. Current speed = 5. Current relative to A = 1/4 * 4k = k = 5. So speed of A = 20, B = 25. Downstream speed of B = 25 + 5 = 30. Distance = 30 * 1.5 = 45 km.