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X is running around a circular track completing one round every 40 seconds. Y running in the opposite direction on the same circular track crosses X e
Question

X is running around a circular track completing one round every 40 seconds. Y running in the opposite direction on the same circular track crosses X every 15 seconds. The time in seconds taken by Y to complete one round is

A.

12

B.

24

C.

30

D.

36

Correct option is B

Given:
X completes one round in 40 seconds
Y runs in the opposite direction and crosses X every 15 seconds
We are to find:
Time taken by Y to complete one round (in seconds)

Concept Used:

When two objects move in opposite directions around a circular track,
they cross each other at intervals of time given by:
Time between meetings = Total distance / Relative speed
Solution:

Let speed of X=140 rounds/sec Let speed of Y=1T rounds/sec Relative speed (opposite direction)=140+1T They meet every 15 seconds=>115=140+1T 1T=115140 =83120=5120=124 T=24 seconds\text{Let speed of X} = \frac{1}{40} \text{ rounds/sec} \\\ \\\text{Let speed of Y} = \frac{1}{T} \text{ rounds/sec} \\\ \\\text{Relative speed (opposite direction)} = \frac{1}{40} + \frac{1}{T} \\\ \\\text{They meet every 15 seconds} \Rightarrow \frac{1}{15} = \frac{1}{40} + \frac{1}{T} \\\ \\\frac{1}{T} = \frac{1}{15} - \frac{1}{40} \\\ \\= \frac{8 - 3}{120} = \frac{5}{120} = \frac{1}{24} \\\ \\T = 24 \text{ seconds}


Final Answer:
S. Ans. (B) 24

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