Walking at 4/5th of his usual speed, a man is 12 minutes late for his office. What is the usual time taken by him to cover that distance?

A. 48 minutes

B. 50 minutes

C. 54 minutes

D. 60 minutes

UPSC CDS 1 2021 Elementary Mathematics Paper

Solution:

Let us have a look at the shortcut method:

Ratio of usual speed to 4/5th speed = 5 : 4

As distance is the same, ratio of usual time to time taken at 4/5th speed = 4 : 5

A difference of 1 unit of time corresponds to 12 minutes time difference, therefore, 4 units of time (usual time) will be 4 * 12 = 48 minutes.

Hence, (a) is the correct answer.

Let us have a look at the basic approach:

Let the usual speed of man be x km/minute.

Let the usual time taken by the man be t minutes.

Let the distance be d km.

We know that,

speed = distance/time

x = d/t

d = x.t .......(1)

If the speed of man becomes 4x/5 km/minute, then the time taken by the man will be (t - 12) minutes

Using, speed = distance/time

4x/5 = d/(t - 12)

d = 4x.(t - 12)/5 ....(2)

Equating equation 1 and 2, we get

x.t = 4x.(t - 12)/5

t = 4(t - 12)/5

5t = 4t - 48

t = 48 minutes.

Hence, (a) is the correct answer.

This is a question from time, speed and distance topic and solved using the concept of ratio and proportion in shortcut method.


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