Question

A person X is running around a circular track completing one round every 40 seconds. Another person Y running in the opposite direction meets every 15 seconds. The time, expressed in seconds, taken by Y to complete one round is

• A. 12.5
• B. 24
• C. 25
• D. 55

Answer 1

Answer: (B)

24

Let the time taken by the other person be $t$

the angle $\theta$ covered by first person in $1$ second $=\frac{2\pi }{40}$

in 15 seconds $=\frac{2\pi }{40}\times 15$

At the same time the other person will cover $\alpha$

$\alpha =\frac{2\pi }{t}\times 15$

As the 2 persons meet

$\theta +\alpha =2\pi \frac{2\pi }{40}\times 15+\frac{2\pi }{t}\times 15=2\pi \frac{3}{8}+\frac{15}{t}=1\frac{15}{t}=\frac{5}{8}t=24$

Option $B$ is correct