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 \(6 \text{ km/h} = \frac{6000}{3600} = \frac{5}{3} \text{ m/s} \)  
Mary's speed is \(7.5 \text{ km/h} = \frac{7500}{3600} = \frac{25}{12} \text{ m/s} \)

Let the track lengths be:

• Track A: \( x \, \text{meters} \)
• Track B: \( y \, \text{meters} \)

Given: \( x + y = 325 \)  .... (1)

Time taken by John to complete 9 rounds of Track A:

\[ \text{Time} = \frac{9x}{\frac{5}{3}} = \frac{27x}{5} \text{ seconds} \]

Time taken by Mary to complete 5 rounds of Track B:

\[ \text{Time} = \frac{5y}{\frac{25}{12}} = \frac{60y}{25} = \frac{12y}{5} \text{ seconds} \]

Since the times are equal:

\[ \frac{27x}{5} = \frac{12y}{5} \Rightarrow 27x = 12y \Rightarrow x = \frac{4}{9}y \]

Substitute into equation (1):

\[ x + y = 325 \Rightarrow \frac{4}{9}y + y = 325 \Rightarrow \frac{13y}{9} = 325 \Rightarrow y = 225 \Rightarrow x = 100 \]

Now, to find the time Mary takes to run one round of Track A:

\[ \text{Time} = \frac{x}{\text{Mary's speed}} = \frac{100}{\frac{25}{12}} = \frac{100 \times 12}{25} = 48 \text{ seconds} \]

Final Answer:

Mary takes 48 seconds to run one round of Track A.