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Ratio of speed (in km/h) of three persons A, B, and C is 5 : 4 : 6, and LCM of the speed of A, B, and C is 480. They started running simultaneously around a circular track of radius 70 m, then after how much time from the start they will meet again at the starting point?

Ratio of speed (in km/h) of three persons A, B, and C is 5 : 4 : 6, and LCM of the speed of A, B, and C is 480. They started running simultaneously around a circular track of radius 70 m, then after how much time from the start they will meet again at the starting point? Correct Answer 3.3 minutes

Given:

Speed ratio (A : B : C) = 5 : 4 : 6

r = 70 m

Formula Used:

The perimeter of circular track = 2πr

Calculation:

Let the speed of A be 5x = 5 × x

Speed of B be 4x = 2 × 2 × x

Speed of C be 2 × 3 × x

⇒ LCM of speed of A, B and C = 5 × 2 × 2 × 3 × x = 480

⇒ 60x = 480

⇒ x = 8

Speed of A, B, and C is 40 km/h, 32 km/h, and 48 km/h respectively.

Perimeter of track = 2 × (22/7) × 70 = 440 meters = 0.44 km

⇒ Time taken by A to complete one round = (0.44/40) × 3600 = 39.6 seconds

⇒ Time taken by B to complete one round = (0.44/32) × 3600 = 49.5 seconds

⇒ Time taken by C to complete one round = (0.44/48) × 3600 = 33 seconds

LCM of 39.6, 49.5 and 33 = 198 seconds

∴ They meet with each other at the starting point after 198 seconds or 3.3 minutes. 

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