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Question

A circular field has a circumference of 360 km. Three cyclists start together and can cycle 48, 60 and 72 km a day, round the field. When will they meet again?

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Solution


GIVEN: A circular field has a circumference of 360 km. Three cyclists start together and can cycle 48, 60, and 72 km a day, round the field.
TO FIND: When they meet again.

In order to calculate the time when they meet, we first find out the time taken by each cyclist in covering the distance.

Number of days 1st cyclist took to cover 360 km = Total distanceDistance covered in 1 day = 36048 = 7.5 = 7510 = 152 days

Similarly, number of days taken by 2nd cyclist to cover same distance = 36060 = 6 days

Also, number of days taken by 3rd cyclist to cover this distance = 36072 = 5 days
Now, LCM of 152, 6 and 5 = LCM of numeratorsHCFof denominators = 301 = 30 days

Thus, all of them will take 30 days to meet again.

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