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Question

# Mr. X decides to travel from Delhi to Gurgaon at a uniform speed and decides to reach Gurgaon after T hr. After 30 km, there is some engine malfunction and the speed of the car becomes 45th of the original speed. So, he travels the rest of the distance at a constant speed 45th of the original speed and reaches Gurgaon 45 minutes late. Had the same thing happened after he travelled 48 km, he would have reached only 36 minutes late. What is the distance between Delhi and Gurgaon?

CAT 2021

A
B
C
D
##### 40 km
Solution

Correct option is

(B)

let the distance from delhi and gurgaon is " x " km

first 30 km ...... travels at usual speed

remaining " x- 30" km .......... travels at reduced speed

To travel "x" km , he usually takes T hrs. , therefore , to travel " x- 30" km , he should take (x-30) T / x hrs

it is given that he travelled only at 4/5th of his usual speed.

because of this , he would have taken 5/4th of the time to travel the remaining distance , which means , he takes 1/4th of the time extra . (this is given to be 45 minutes)

$1/4*(x-30)T/x&space;&space;=&space;3/4...........(1)$

the same thing happened after he travelled 48 km , he would have reached only 36 minutes or 34 hrs late . hence

$1/4*(x-48)T/x&space;&space;=&space;3/5...........(2)$

on dividing , we get x = 120 km

so , B is the correct option