In a circular race of 800 m length, Ram and Mohan start at speeds of 25 m/sec and 40 m/sec, respectively, at the same time from the same point. After how much time will they meet for the first time at the starting point, when running in the same direction?

Question

Question

This question was previously asked in

SSC GD Constable 2025 Official Paper (Held On: 07 Feb, 2025 Shift 1)

Answer 1

Given:

Length of the circular track = 800 m

Ram's speed = 25 m/sec

Mohan's speed = 40 m/sec

Direction of running = Same direction

Formula used:

Time = Distance / Speed

To meet at the starting point, the time will be the LCM of the individual times taken to complete one round.

Calculations:

Time taken by Ram to complete one round (T_Ram) = 800 m / 25 m/sec = 32 seconds

Time taken by Mohan to complete one round (T_Mohan) = 800 m / 40 m/sec = 20 seconds

To find when they will meet for the first time at the starting point, we need to find the LCM of their individual times to complete one round.

Time to meet at the starting point = LCM(T_Ram, T_Mohan)

⇒ Time to meet at the starting point = LCM(32, 20)

Prime factorization of 32 = 2⁵

Prime factorization of 20 = 2² × 5

LCM(32, 20) = 2⁵ × 5 = 32 × 5 = 160 seconds

∴ They will meet for the first time at the starting point after 160 seconds.