An athlete runs to and fro between points A and B at a speed of 10 km/h. A second athlete simultaneously runs from point B to A and back at a speed of 15 km/h. If they cross each other 12 min after the start, after how much time will they cross each other again?

18 min

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24 min

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36 min

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48 min

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Solution

The correct option is B 24 min
For first meeting, Distance to be covered = D, time taken = 12 min
For second meeting, Distance to be covered (After first meeting, till second meeting) = 2D
$∴$ Time required to cross again = $2 \times 12 = 24 m i n .$

Alternate Approach:

Both the athlete are crossing each other after 12 min, which means that the distance between them is 5 km (Relative speed = 25km/h and time taken for first meet = 12 min = 1/5 hours). Now they have to cover 10 km after the first meet for meeting second time.
Time required = (10 km)/ (25km/h) = 2/5 hours = 24 min.

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