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

The Correct Option is A

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.