CAT 2019 Question Paper (Slot 2) - QUANT Question 20

Question 20

John jogs on track A at 6 kmph and Mary jogs on track B at 7.5 kmph. The total length of tracks A and B is 325 metres. While John makes 9 rounds of track A, Mary makes 5 rounds of track B. In how many seconds will Mary make one round of track A?

Correct Answer: 48


Speed of John = 6kmph 

Speed of Mary = 7.5 kmph 

Lengths of tracks A and B = 325 m

Let the length of track A be a, then the length of track B = 325-a

9 rounds of John on track A = 5 rounds of Mary on track B

$$\ \frac{\ 9\times\ a}{6\ \times\ \ \frac{\ 5}{18}}\ =\ \ \frac{\ 5\cdot\left(325-a\right)}{7.5\times\ \ \frac{\ 5}{18}}$$

On solving we get , 13a=1300


The length of track A = 100m, track B = 225m

Mary makes one round of track A = $$\ \frac{\ 100}{7.5\times\ \ \frac{\ 5}{18}}$$

= 48 sec

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