Racer A and racer B run a race of 18 km on a circular track of length 800 m. Both complete one round in 200 sec and 250 sec, respectively. After how much time from the start will the faster person meet the slower person for the last time?

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 17 Jul 2023 Shift 4)

Answer 1

Given:

Total race between A and B = 18 km

Length of a circular track = 800 m

Time taken by A to complete the 1st round = 200 sec

Time taken by B to complete the 1st round = 250 sec

Formula used:

Distance = speed × time

Calculation:

Total race between A and B = 18 km = 18000 m

Number of rounds to complete the race = 18000/800 = 22.5 rounds

Time taken by A to complete the 1st round = 200 sec

For 22.5 round = 200 × 22.5 = 4500 sec.

When A and B start running,

The first meeting will occur at L.C.M (200, 250) = 1000 sec.

Fourth meet will be = 1000 × 4 = 4000 sec.

For the next meeting,

Time would be 5000 sec, which is impossible as A completes the race in 4500 sec.

But, to complete 22.5 rounds A takes 4500 sec. So the time cannot be more than 4500 sec.

So, the faster person meets the slower person at 4000 sec.

∴ The correct option is 2.

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