Question

Prakash and Pramod are running along a circular
track having started at the same time from the same
point, in the same direction. How much more
distance would Prakash have travelled compared to
Pramod by the time they meet for the 11th time given
that the radius of the track is 7 m, Prakash and
Pramod run at 22 m/s and 11 m/s respectively?
(in m)​

Answer 1

Given :- Prakash and Pramod are running along a circular track having started at the same time from the same point, in the same direction. How much more distance would Prakash have travelled compared to Pramod by the time they meet for the 11th time given that the radius of the track is 7 m, Prakash and Pramod run at 22 m/s and 11 m/s respectively ? (in m)

Solution :-

from given data we have :-

• Radius of Track = 7m. Therefore, circumference of circle = 2 * π * radius => 2 * (22/7) * 7 = 44m.
• Speed of prakash = 22m/s.
• Speed of Parmod = 11m/s.

we know that,

• Time taken to meet for the 1st time at starting point, T = LCM (Time taken by them to complete one round.)

So,

→ Time taken by Prakash to complete one round = Length of the circular track / speed of Prakash = 44/22 = 2 seconds.

and,

→ Time taken by Pramod to complete one round = Length of the circular track / speed of Prakash = 44/11 = 4 seconds.

Than,

→ Time taken to meet for the 1st time at starting point, T = LCM of (4 and 2) = 4 seconds.

Thus, they meet at starting point after every 4 seconds.

Now,

→ for 11th time total time = 4 * 11 = 44 seconds.

Therefore,

→ Prakash has covered in 44 seconds = 44/2 = 22 rounds.

→ Parmod has covered in 44 seconds = 44/4 = 11 rounds.

Hence,

→ Prakash has covered = 22 - 11 = 11 rounds more than Parmod.

∴

→ Distance more distance Prakash would have travelled compared to Pramod = 11 * 44 = 484 m. (Ans.)

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