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 train covers a certain distance in two halves. It travels at 210 km/hr for the first half and at 240 km/hr for the second half. If the train takes 20 hours to finish the journey, find the total distance travelled.

  1. 4480 km

  2. 4000 km

  3. 3600 km

  4. 4500 km

  5. 5480 km
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let total distance be D. Time for first half = (D/2) / 210 = D/420. Time for second half = (D/2) / 240 = D/480. Total time = D/420 + D/480 = 20. D(8+7)/3360 = 20 => 15D/3360 = 20 => D = (20*3360)/15 = 4480.

Multiple choice

A toy car was moving; and after it had travelled 9 miles, a dog started chasing it with double the speed of the car from the same point the car had left. Find the distance from the starting point in which the dog would catch the car.

  1. 10 miles

  2. 18 miles

  3. 20 miles

  4. 25 miles

  5. 35 miles
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the car speed be v. The dog's speed is 2v. The car has a 9-mile head start. Time for dog to catch car = (Head start distance) / (Relative speed) = 9 / (2v - v) = 9/v. Distance covered by dog = Speed * Time = 2v * (9/v) = 18 miles.

Multiple choice

Ratio of speeds of three cars is 3 : 6 : 8. Calculate the ratio of time taken by these cars, if they cover the same distance.

  1. 4 : 8 : 3

  2. 3 : 8 : 4

  3. 8 : 4 : 3

  4. 8 : 3 : 4

  5. 4 : 3 : 8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Since speed is inversely proportional to time for a constant distance, the ratio of time taken is the inverse of the ratio of speeds. The inverse of 3:6:8 is 1/3 : 1/6 : 1/8. Multiplying by the least common multiple (24) gives 8 : 4 : 3.

Multiple choice

Mr. A has to catch a flight whose boarding time is 10:00 am. He calculated that if he has to reach there on time, he will have to drive his car at a speed of 40 km/hr from his home and if he has to reach the airport 2 hours early, then he will have to drive at speed of 60 km/hr. Calculate the speed at which he has to travel such that he reach the airport one hour early?

  1. 48 kmph

  2. 50 kmph

  3. 52.5 kmph

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let D be the distance. Time at 40 km/hr is D/40. Time at 60 km/hr is D/60. The difference is 2 hours: D/40 - D/60 = 2. D/120 = 2, so D = 240 km. To reach 1 hour early (compared to 40 km/hr), he needs to take (D/40 - 1) hours. Time = 6 - 1 = 5 hours. Speed = 240 / 5 = 48 km/hr.

Multiple choice

A couple drives in a car from place A to place B. For 2/3 of the distance between places A and B, the husband drives at 40 km/hr and for the remaining distance he drives at 60 km/hr. Find the average speed of the car.

  1. 45 km/hr

  2. 50 km/hr

  3. 52.5 km/hr

  4. 48 km/hr

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

Average speed = Total distance / Total time. Let total distance be 3D. Time = (2D/40) + (D/60) = D/20 + D/60 = 4D/60 = D/15. Average speed = 3D / (D/15) = 45 km/hr.

Multiple choice

The distance between two stations A and B is 138 km. A train starts from A towards B and another from B to A at the same time and they meet after 6 hours. The train travelling from A to B is slower by 7 kmph compared to other train from B to A, then find the speed of the slower train?

  1. 8

  2. 9

  3. 10

  4. 11
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let speeds be v and v+7. Relative speed = 2v+7. Distance = 138, time = 6. 6(2v+7) = 138. 2v+7 = 23. 2v = 16, v = 8.

Multiple choice

A car driver covers a distance between two cities at a speed of 60 kmph and on the return his speed is 40 kmph. He goes again from the 1st to the 2nd city at twice the original speed and returns at half the original return speed. Find his average speed for the entire journey.

  1. 35

  2. 40

  3. 45

  4. 50
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Average speed = Total distance / Total time. Let distance between cities be D. Time 1 = D/60, Time 2 = D/40, Time 3 = D/120, Time 4 = D/20. Total time = D(1/60 + 1/40 + 1/120 + 1/20) = D(2/120 + 3/120 + 1/120 + 6/120) = 12D/120 = D/10. Total distance = 4D. Average speed = 4D / (D/10) = 40 kmph.

Multiple choice

Directions: The given question is followed by three statements numbered I, II and III. Read all the statements to find the answer to the given question. Choose which of the given statements is/are required to answer the question. What is the speed of the boat in still water? I. The boat can cover 15 km distance upstream in 3 hours. II. The boat can cover 30 km distance downstream in 2 hours. III. The boat can cover 30 km upstream and 15 km downstream in 7 hours.

  1. Only I

  2. Only II and III

  3. Only I and II

  4. Any two of the given three

  5. All three statements together cannot give the answer.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let u be speed upstream and v be speed downstream. Statement I gives u = 15/3 = 5 km/hr. Statement II gives v = 30/2 = 15 km/hr. Still water speed = (v+u)/2 = (15+5)/2 = 10 km/hr. Statement III also allows finding u and v. Any two statements are sufficient.

Multiple choice

In a motorcycle race, one of the three motorbikes that started out at the same time was at 15 kmph less than the first one and 3 kmph more than the third one. It arrived at the terminal point 12 minutes after the first motorbike and 6 minutes before the third one. There were no stops en route. What is the time taken by the third motorbike?

  1. 30 min

  2. 1 h

  3. 1 h 12 min

  4. 1 h 15 min
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the speeds be v1, v2, v3. We have v2 = v1 - 15 and v2 = v3 + 3. Using time = distance/speed and the time differences (12 min = 0.2 h, 6 min = 0.1 h), we set up equations for the distance D: D/v2 - D/v1 = 0.2 and D/v3 - D/v2 = 0.1. Solving these yields the time taken by the third motorbike.

Multiple choice

Points A and B are 90 km apart from each other on a highway. A car starts from A and another from B at the same time. If they go in opposite directions, they meet in 9/7 hours. If they go in the same direction, they meet after 9 hrs. Find their speeds (in km/hr).

  1. 40, 30

  2. 40, 50

  3. 60, 30

  4. 50, 60
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let speeds be x and y. Opposite: (x+y) = 90 / (9/7) = 70. Same direction: (x-y) = 90 / 9 = 10. Adding: 2x = 80 -> x = 40. Subtracting: 2y = 60 -> y = 30.

Multiple choice

Vishnu travelled equal distances at speeds of 10 km/hr, 30 km/hr and 8 km/hr, respectively and took a total of 15.5 minutes to complete. Find the total distance he travelled (in km). বিষ্ণু যথাক্রমে 10 কিমি / ঘন্টা, 30 কিমি / ঘন্টা এবং 8 কিমি / ঘন্টা গতিতে সমান দূরত্ব ভ্রমণ করেছিলেন এবং ভ্রমণ সম্পূর্ণ করতে 15 মিনিট সময় নিয়েছিলেন। তিনি মোট দূরত্ব (কিমি ) ভ্রমণ করেছেন?

  1. 1

  2. 3

  3. 4

  4. 2
Reveal answer Fill a bubble to check yourself
B Correct answer