CAT 2016 Quantitative Ability

Question : 6 of 34

Marks: +1, -0

Two friends - Prakash and Arpit - started running simultaneously from a point P in the same direction along a straight running track. The ratio of the speeds of Prakash and Arpit was 2 :5 respectively. Two hours later, Arpit turned back and started running backwards at one-fifth of his original speed. He met Prakash at a distance of 10 km from the point P. What was Prakash’s speed?

1.25 km/hr
2.5km/hr
3.75 km/hr
6.25 km/hr

Validate

Solution:

Let the speeds of Prakash and Arpit be 2x and 5xrespectively. Let’s assume that Arpit turned back frompoint Q as shown in the figure given below, ran at aspeed of x after turning back and met Prakash atpoint R, ‘t’ hours after they started running

From the given conditions,

2x × t = 10 = 5x × 2 - x × (t - 2)

=> t = 4
So the running speed of Prakash

=2x

=\;\;{10}/{4}=2.5 {km}\/ {hr}

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