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?
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?
Updated On: Jul 28, 2025
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The Correct Option is A
Solution and Explanation
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.
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