Two runners, Sony and Mony, start running on a circular track of length 200 m at speeds of 18 and 24 km/h, respectively, in the same direction. After how much time from the start will they meet again at the starting point?

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 14 Jul 2023 Shift 1)

Answer 1

Given:

Sony and Mony, start running on a circular track of length 200 m at speeds of 18 and 24 km/h, respectively, in the same direction.

Formula used:

When two runners run on a circular track of length D m at a m/sec and b m/sec, respectively, in the same direction.

Time taken by them to meet for the first time at starting point on the track

⇒ LCM (D/a , D/b)

Calculation:

The speed of Sony (S₁) = 18 km/hr

⇒ 18 x (5/18) = 5 m/sec

The speed of Mony (S₂) = 24 km/hr

⇒ 24 x (5/18) = 20/3 m/sec

Time taken by them to meet for the first time at the starting point on track

⇒ LCM (D/a , D/b)

⇒ LCM (200/5, 200/(20/3))

⇒ LCM (40, 30)

40 = 2 x 2 x 2 x 5

30 = 2 x 3 x 5

⇒ LCM (40, 30) = 2 x 2 x 2 x 3 x 5 = 120 seconds

∴ The required time is 120 seconds.

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