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Quantitative Reasoning – Practice – Bill and John walk towards each other!

PSA_PRACTICE_QNR29. John and Bill walk towards to each other’s house. If both leave at 10 am, they meet 10 minutes later. If Bill leave 3 minutes later then John, they’ll meet 9 minutes after Bill leaves. How long does it take for Bill to walk to John’s house?

1) 10 minutes

2) 12 minutes

3) 15 minutes

4) 16 minutes

Ans:

Let, John’s and Bill’s houses be A & B respectively and they meet at ‘M’ in the first scenario.

A|———————–M————–|B

Let, John’s and Bill’s speed be ‘j’ and ‘b’ units/minute.

AB= AM+ MB= 10j + 10b= 10(j+b) ……….. (Y)
A|——————————-N——|B

Let, in the second case both meet at point ‘N’; when they meet, John has walked for 12 minutes and Bill for 9 minutes.

AB= AN + NB = 12j + 9b ………..(Z)
From, (Y) & (Z),

10j + 10b = 12j + 9b

=> b= 2j

Using (Y)= AB= 10(3b/2) = 15b
Since, Bill’s speed = b, time taken to cover this distance= 15 minutes. Option (3).

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