Three men Ram, Karan and Mohan run around an oval garden from a fixed post at the rates of 5, 5 1⁄ 7, 5 1⁄ 3 per hour. They come back to the fixed post in 3 3⁄ 4 hours. Find the greatest length, the race course can have.

28 / 5 km
5 / 28 km
11 / 28 km
28 / 11 km

Correct Answer: 5 / 28 km

Explanation:

Total number of rounds made by Ram in 15 / 4 hrs = 5 × 15 / 4 = 75 / 4
∴ Total number of rounds made by Karan in 15 / 4 hrs = 36 / 7 * 15 / 4 = 135 / 7
Total number of rounds made by Mohan in 15 / 4 hrs = 16 / 3 * 15 / 4 = 20
H.C.F. of 75 / 4 , 135 / 7 and 2 = 5 / 28

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