Question

A person $X$ is running around a circular track completing one round every $40 \,s$. Another person $Y$ running in the opposite direction meets $X$ every $15\, s$. 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)

Given,
$X$ complete one round in $40\, s$.
$\therefore 2 \pi=40\, s$

In one second, he complete, $\left(\frac{2 \pi}{40}\right)$ round
In $15 \,s$, he complete $\left(\frac{2 \pi \times 15}{40}\right)$ round
Let $Y$ complete one round in $t\, s$
$\therefore 2 \pi=t$
In one second $Y$ complete $\left(\frac{2 \pi}{t}\right)$ round
In $15 \,s , Y$ complete $\left(\frac{2 \pi}{t}\right) \times 15$ round
Since, both are move in opposite direction.
$\therefore \frac{2 \pi}{40} \times 15+\frac{2 \pi}{t} \times 15=2 \pi$
$\Rightarrow 15\left(\frac{1}{40}+\frac{1}{t}\right)=1$
$\Rightarrow \frac{1}{t}=\frac{1}{15}-\frac{1}{40}$
$\Rightarrow \frac{1}{t}=\frac{8-3}{120}$
$=\frac{5}{120}=\frac{1}{24}$
$\therefore t=24\, s$