# CAT2019-2: 76

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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 $A$?______

edited

Ans is (48)

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

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

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

Solving these two equations ,we get  $x=100mtr$

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

238 points 2 2 4

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