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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?

Explanation:

Let the track length for John be 'a' and for Mary be 'b'

So, Distance travelled by John = 9a

Distance travelled by Mary = 5b

Now, Time taken by John = 9a/6 hours

Time taken by Mary = 5b/7.5 hours

We know that Time taken by John = Time taken by Mary

⇒ 9a/6 = 5b/7.5

⇒ a = 4b/9

Total track length = 325 meters

So, 4b/9 + b = 325 meters

⇒  13b/9 = 325 meters

⇒ b = 225 meters

⇒ a = 100 meters

Mary jogs at 7.5 Kmph = 7.5 × 5/18

So, time taken = $\frac{100}{(7.5\times {\displaystyle \frac{5}{18}})}$ = 48 seconds.

Hence, 48.