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CAT 2019 Quant Question with Solution 44

Question:
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?

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Correct Answer: 48

Speed of John = 6kmph = $6\times \frac{5}{18}=\frac{5}{3}m/s$

Speed of Mary = 7.5 kmph = $7.5\times \frac{5}{18}=\frac{25}{12}m/s$

Let the track length of A and B be x and y respectively.

Given, x + y = 325 …. (1)

Time taken by John to cover one round of A = $\frac{x}{5/3}\sec $

Therefore, time taken to cover 9 rounds = $9\times \frac{x}{5/3}=\frac{27}{5}x\ \sec $

Time taken by Mary to cover one round of B = $\frac{y}{25/12}\sec $

Therefore, time taken to cover 5 rounds = $5\times \frac{y}{25/12}=\frac{12}{5}y\ \sec $

As per the condition:

$\frac{27}{5}x=\frac{12}{5}y$

$\Rightarrow \frac{x}{y}=\frac{12}{27}=\frac{4}{9}$

Putting in equation (1) we get x=100 and y =225.

Time taken by Mary to cover one round of A=$\frac{100}{25/12}=48\ \sec $


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