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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 30x−30y=3 ⇒10x−10y=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, 30y−302x=112 ⇒30y−302x=32 ⇒10y−5x=12 ⇒−10x+20y=1 ...(ii) Let 1x=u and 1y=v. In equation (i) and (ii), we get: 10u−10v=1⇒10u−10v−1=0......(iii) and −10u+20v=1⇒−10u+20v−1=0.....(iv) Adding equations (iii) and (iv), we get 10v−2=0⇒v=15 Putting v=15 in equation (iii), we get ⇒10u−1015−1=0 ⇒10u−3=0⇒u=310 Now,u=310 ⇒1x=310 ⇒x=103 ∴ X's speed is 103km/hr.

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