This set of Aptitude Questions and Answers (MCQs) focuses on “Time and Distance – Set 3”.
1. A man travelled first half of his journey at a speed of 40 kmph and the second half of his journey at a speed of 35 kmph. Find the average speed of the man.
a) 35 kmph
b) 37.5 kmph
c) 40 kmph
d) 42.5 kmph
View Answer
Explanation: The average speed of the man = the average of both the speeds (here it is the average of both the speeds because the distance travelled with respective speeds is equal).
The average speed = 40 + 35 / 2 = 75 / 2 = 37.5 kmph
2. A man travelled 40% of his journey at a speed of 50 kmph and the rest of his journey at a speed of 80 kmph. Find his average speed throughout the journey.
a) 60 kmph
b) 66 kmph
c) 68 kmph
d) 74 kmph
View Answer
Explanation: The average speed of the man = [(40 * 50) + (60 * 80)] / 100 = (2000 + 4800) / 100 = 6800 / 100 = 68 kmph
3. If a man travelled at 6 / 7th of his usual speed the time taken by him to cover the usual distance is what percentage of the usual time taken?
a) 116.6%
b) 133.3%
c) 166.6%
d) 200%
View Answer
Explanation: Here the distance travelled is same as the usual distance so the time taken will be reciprocal of the speed.
The time taken = 1 / (6 / 7) = 7 / 6th of the usual time = 7 / 6 * 100 = 116.6 % of the usual time taken.
4. Travelling at 3 / 7th of his usual speed a man is late by 21 minutes. What is the usual time taken by him to cover the same distance?
a) 15 minutes
b) 15.25 minutes
c) 15.50 minutes
d) 15.75 minutes
View Answer
Explanation: Let the distance be d and the usual distance be 7x.
d / 3x – d / 7x = 21 / 60
(7d – 3d) / 21x = 21 / 60
4d / 21x = 21 / 60
240d = 441x
Usual speed = d / 7x
D = 441x / 240
Usual speed = 441x / (240 * 7x) hours
Usual speed = 63 / 240 hours = 63 / 4 minutes = 15.75 minutes
5. The ratio of speeds of p : q : r is 3 : 4 : 5. Find the ratio of time taken by p, q and r to cover j km.
a) 5 : 4 : 3
b) 4 : 3 : 2
c) 12 : 15 : 20
d) 20 : 15 : 12
View Answer
Explanation: The distance covered = j
Let the speeds be in terms of x.
The speeds = 3x, 4x and 5x
The time taken = j / 3x, j / 4x and j / 5x
Let j be 60
The time taken = 20 / x, 15 / x and 12 / x
The ratio of time taken = 20 / x : 15 / x : 12 / x = 20 : 15 : 12
6. A man travels 10 km at a speed of 20 kmph, 20 km at a speed of 30 kmph and 50 km at a speed of 60 kmph. Find the time taken throughout the journey.
a) 1 hour
b) 1.5 hours
c) 2 hours
d) 2.5 hours
View Answer
Explanation: The time taken = 10 / 20 + 20 / 30 + 50 / 60 = 0.5 + 0.66 + 0.83 = 1.99 hours ≈ 2 hours.
6. A man travels 60 km at a speed of 20 kmph 70 km at a speed of 120 kmph and 50 km at a speed of 35 kmph. Find the time taken throughout the journey.
a) 4 hours
b) 4.5 hours
c) 5 hours
d) 5.5 hours
View Answer
Explanation: The time taken throughout the journey = 60 / 20 + 70 / 120 + 50 / 35 = 3 + 0.583 + 1.428 = 5.01 hours ≈ 5 hours.
7. The ratio of speeds of p : q : r is 6 : 7 : 8. Find the ratio of their time taken.
a) 21 : 24 : 28
b) 28 : 24 : 21
c) 12 : 14 : 18
d) 18 : 14 : 12
View Answer
Explanation: Let the distance be 336 km.
Let the speeds be in terms of x.
The time taken by p, q and r = 336 / 6x, 336 / 7x and 336 / 8x = 56 / x, 48 / x and 42 / x
The ratio of time taken by p, q and r = 56 / x : 48 / x : 42 / x = 56 : 48 : 42 = 28 : 24 : 21
8. If a man travels at 9 / 13th of his usual speed the time taken by him is what percentage of the usual time taken to cover the same distance?
a) 144.4%
b) 122.2%
c) 111.1%
d) 109.9%
View Answer
Explanation: The fraction of time taken is reciprocal of the fraction of speed.
The time taken = 13 / 9th of the usual time taken = 13 / 9 * 100% of the usual time taken = 144.4%
9. A man travels at a speed of 30 kmph for 30% of his journey and at a speed of 80 kmph for the rest of his journey. Find his average speed throughout the journey.
a) 60 kmph
b) 65 kmph
c) 70 kmph
d) 75 kmph
View Answer
Explanation: The average speed of the man = (30 * 30 + 70 * 80) / 100 = (900 + 5600) / 100 = 6500 / 100 = 65 kmph
10. A man travels at a speed of 55 kmph for 1 hour and 75 kmph for 7 hours. Find his average speed.
a) 72.5 kmph
b) 75 kmph
c) 77.5 kmph
d) 80 kmph
View Answer
Explanation: The total distance covered = 1 * 55 + 75 * 7 = 55 + 525 km = 580 km
The total time taken = 8 hours
The average time taken = 580 / 8 = 72.5 kmph
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