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

There are two stations 'A' and 'B'. A train from station 'A' with a speed of 60 km/hr moved towards station'B'. Simultaneously, a train from station B moves towards station 'A' with a speed of 40 km/hr. From station B trains are leaving at a fixed interval of 'n' minutes. The train from 'A' and first train from 'B' meets after half an hour. The train from A meets a total of 6 trains from B till it reaches station 'B'. What is the value of 'n' if last train met was just at station 'B'

  1. 15

  2. 10

  3. 5

  4. 6

  5. 18
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

A person travelled the distance of 220 km from point A to B at an average speed of 66 km/hr. The person travelled first 75 km at an average speed of 55 km/hr. For the rest of the distance, he covered some distance at 75 km/hr and remaining distance at 65 km/hr. Find the distance (in km rounded off to the nearest integer) which was travelled at a speed of 65 km/hr.

  1. 15

  2. 16

  3. 17

  4. 18
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total distance = 220 km. Average speed = 66 km/hr. Total time = 220/66 = 10/3 hours. First 75 km at 55 km/hr = 75/55 = 15/11 hours. Remaining distance = 220 - 75 = 145 km. Remaining time = 10/3 - 15/11 = (110 - 45) / 33 = 65/33 hours. Let d be distance at 65 km/hr, then (145-d) is at 75 km/hr. Time = d/65 + (145-d)/75 = 65/33. Solving: 15d + 13(145-d) = (65/33) * 975. 2d + 1885 = 1920.3. 2d = 35.3. d = 17.65. Rounded = 18.

Multiple choice

The distance between two stations P and Q is 982 Km. A train covers journey from P to Q at 90 km/hr and returns back to P with uniform speed of 49 km/hr. Find the average speed of train during the whole journey

  1. 71 km/hr approx.

  2. 63 km/hr approx.

  3. 75 km/hr approx.

  4. 69 km/hr approx.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Average speed for a round trip is (2 * v1 * v2) / (v1 + v2). Here v1 = 90, v2 = 49. Average speed = (2 * 90 * 49) / (90 + 49) = 8820 / 139 = 63.45 km/hr, which is approximately 63 km/hr.

Multiple choice

At 8:00 am, a boy starts from point P, at a speed of 40 mph, to go to point Q. At 10:00 am, a man starts from point P, to make the same journey. He passes the boy at a distance of 200 miles from point P. Quantity A Quantity B Speed of the man 80 mph

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Boy travels for 2 hours (8am to 10am) at 40 mph = 80 miles. Distance remaining = 200 - 80 = 120 miles. Man covers 120 miles in the same time the boy covers 120 miles. Boy time = 120 / 40 = 3 hours. Man speed = 120 / 3 = 40 mph. Quantity A (40) < Quantity B (80).

Multiple choice

A train meets with an accident after travelling 30 km, after which it moves with4/5th of its original speed and arrives at the destination 45 minutes late. Had the accident happened 18 km further on, it would have been reached the destination 9 minutes before the time in the first case. Find the original speed of the train.

  1. 25 kmph

  2. 15 kmph

  3. 30 kmph

  4. 7.5 kmph
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let original speed be v. After 30km, distance D remains. Time taken = D/v. New time = D/(0.8v). Difference = 0.25(D/v) = 45 min = 0.75 hr. D/v = 3 hr. If accident was 18km later, distance D-18 remains. Time saved = 9 min = 0.15 hr. 0.25(D/v) - 0.25((D-18)/v) = 0.15. 0.25(18/v) = 0.15. 4.5/v = 0.15. v = 30 kmph.

Multiple choice

A motor boat covers a certain distance downstream in 30 minutes, while it comes back in 45 minutes. If the speed of the stream is 5 kmph what is the speed of the boat in still water?

  1. 10 kmph

  2. 25 kmph

  3. 20 kmph

  4. 15 kmph
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let boat speed be B and stream speed be S = 5. Downstream speed = B+5, Upstream speed = B-5. Distance = (B+5) * (30/60) = (B-5) * (45/60). 0.5(B+5) = 0.75(B-5). B+5 = 1.5(B-5). B+5 = 1.5B - 7.5. 0.5B = 12.5. B = 25 kmph.

Multiple choice

A train travels from City X to City Y which are 840 km apart and in different time zones at an average speed of 60 kmph and arrives in City Y at 6:00 in the evening (City Y time). At what hour in the morning (City X time), did the train depart for City Y? (Note: The time in City X is an hour ahead of time in City Y)

  1. 4:00

  2. 5:00

  3. 6:00

  4. 7:00
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The train travels 840 km at 60 kmph, taking 14 hours. It arrives at 18:00 (City Y time). Since City X is one hour ahead, 18:00 in City Y is 19:00 in City X. Subtracting the 14-hour travel time from 19:00 gives 5:00 in the morning in City X.

Multiple choice

The distance travelled by a person in 9 hours is 610 km. Some of the portion of his journey is travelled in a bus running at 40 km/hr and remaining in a train running at 90 km/hr. How much distance has the person travelled by bus?

  1. 160 km

  2. 210 km

  3. 150 km

  4. 200 km

  5. 110 km
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let x be the distance by bus and (610-x) by train. Time = x/40 + (610-x)/90 = 9. Multiply by 360: 9x + 4(610-x) = 3240. 9x + 2440 - 4x = 3240. 5x = 800. x = 160 km.

Multiple choice

Directions: Solve the following question and mark the best possible option. On a journey across Bombay, a tourist bus averages 10 km/h for 20% of the distance, 30 km/h for 60% of it and 20 km/h for the remainder. The average speed for the whole journey was

  1. 10 km/h

  2. 30 km/h

  3. 5 km/h

  4. 20 km/h

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

Average speed = Total Distance / Total Time. Let distance be 100 km. Time = (20/10) + (60/30) + (20/20) = 2 + 2 + 1 = 5 hours. Average speed = 100 / 5 = 20 km/h.