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Question

X takes 3 hours more than Y to walk 30 km. But if X doubles his pace, he is ahead of Y by 1.5 hours. The speed of X is:


A

5 km/hr

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B

9 km/hr

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C

97 km/hr

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D

103 km/hr

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Solution

The correct option is D

103 km/hr


Let the speed of X and Y be x km/hr and y km/hr respectively.

Then, the time taken by X to cover 30 km
=30xhr

and time taken by Y to cover 30 km
=30yhr

By the given conditions, we have

30x30y=3

10x10y=1 ...(i)

If X doubles his pace then the speed of X is 2x km/hr.

Time taken by X to cover 30 km =302xhr

We have,

30y302x=112

30y302x=32

10y5x=12

10x+20y=1 ...(ii)

Let 1x=u and 1y=v.

In equation (i) and (ii), we get:

10u10v=110u10v1=0......(iii)

and 10u+20v=110u+20v1=0.....(iv)

Adding equations (iii) and (iv), we get

10v2=0v=15

Putting v=15 in equation (iii), we get

10u10151=0

10u3=0u=310

Now,u=310

1x=310

x=103

X's speed is 103km/hr.


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