A hunter fired two shots from the branch of a tree at an interval of 76 seconds. A tiger separating too fast hears the two shots at an interval of 83 seconds. If the velocity of the sound is 1195.2 km/h, then find the speed of the tiger.

112.8 km/h

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100.8 km/h

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80.16 km/h

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None of these

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Solution

The correct option is B 100.8 km/h
This case can also be interpreted as the tiger starting running after the first shot is fired.
If the tiger is not running then he must have heard the second shot after 76 seconds.
So, distance covered by the tiger in 83 seconds is equal to the distance covered by the bullet in 7 seconds.
Let speed of tiger be x kmph.
Hence, $1195.2 \times \frac{5}{18} \times 7 = x \times \frac{5}{18} \times 83$ .
On solving we get x = 100.8 kmph.

Alternate Approach:
In case of increasing gap between two objects .
$\frac{S p e e d o f s o u n d}{S p e e d o f t i g e r} = \frac{T i m e u t i l i z e d}{D i f f e r e n c e i n t i m e}$
$\frac{1195.2}{x} = \frac{83}{7}$
$\Rightarrow$ x = 100.8 km/h

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