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CAT 2019 Set-2 | Question: 76

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

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Ans is (48)

Let the lengths of tracks A and B be $x,y$ respectively.

Speed of John and Mary in m/s : $\frac{5}{3},\frac{25}{12}\;\left(\text{by multiplying speed in km/h by}\; \frac{5}{18} \right)$

Given  $x+y=325$  and  $\frac{9x}{\frac{5}{3}}=\frac{5y}{\frac{25}{12}}$

Solving these two equations , we get  $x=100\;\text{mtr}$

$\therefore$ Time taken by Mary to complete track A :   $\frac{100\;\text{mtr}}{\frac{25}{12}\text{m/s}}=48$  seconds.

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