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?

• A. 48
• B. 38
• C. 45
• D. 22

Answer 1

Answer: (A)

48

Answer 2

John's speed is $6 km/h,$ which is equivalent to $\frac{5}{3}$ m/s.
Mary's speed is $7.5 km/h$, which is equivalent to $\frac{25}{12} m/s$.
Let the track lengths of A and B be x and y respectively.

Given: $x+y=325 .... (1)$
The time taken by John to cover one round of A is $\frac{x}{\frac{5}{3}}$ seconds.
Therefore, the time taken to cover 9 rounds is $\frac{9x}{\frac{5}{3}}=\frac{27x}{5}$​ seconds.
The time taken by Mary to cover one round of B is $\frac{y}{\frac{25}{12}}$​ seconds.
Therefore, the time taken to cover 5 rounds is $\frac{5y}{\frac{25}{12}}=\frac{12y}{5}$​ seconds.

As per the condition, $\frac{27x}{5}=\frac{12y}{5}$​, which simplifies to $x=\frac{4}{9}y.$
Putting this into equation (1), we get $x=100$ and $y=225$.
The time taken by Mary to cover one round of A is $\frac{100}{\frac{25}{12}}=48$ seconds.