Question

A man beats drum at a certain distance from the mountain. He slowly increases the rate of beating and finds that the echo is not heard distinctly, when the drum beating is at the rate of $40$ per minute. He moves by $80m$ towards the mountain and finds that the echo is again not heard distinctly when the rate of beating of the drum is $1$ per second. What is the original distance of the man from the mountain?

• A. $120m$
• B. $240m$
• C. $270m$
• D. $340m$

Answer 1

Answer: (B)

$240m$

Echo is not heard distinctly, when next beat overlaps with echo simultaneously.
Time per beat $=$ time taken by reflected beat to reach listener.
d being the distance and drum beating at rate of $40$ per minute.
$\frac{2d}{v}=\frac{60}{40}=\frac{3}{2}$
and $\frac{2d-80}{v}=1$
Solving we get $d=240m$