Question

A train approaches a tunnel AB. Inside the tunnel is a cat located at a point that is 3/8 of the distance AB measured from the entrance A. When the train whistles, the cat runs. If the cat moves to the entrance of the tunnel A, the train catches the cat exactly at the entrance. If the cat moves to the exit B, the train catches the cat exactly at the exit. The speed of the train is greater than the speed of the cat by what order ?

• A. 3 : 1
• B. 4 : 1
• C. 5 : 1
• D. None of these

Answer 1

The correct option is B 4 : 1

Let Distance between Train and Entrance of Tunnel when the Train Whistles be $x$ and Length of Tunnel be $AB$

Let speed of Train and Cat be $T$ and $C$ respectively

When The cat moves Towards the Entrance

$\Rightarrow \frac{x}{T}=\frac{3}{8}\times \frac{AB}{C}.....................\left(1\right)$

When the Cat Move Towards the Exit

$\Rightarrow \frac{x+AB}{T}=\frac{5}{8}\times \frac{AB}{C}.......................\left(2\right)$

On Dividing Equation(1) by Equation(2) we get

$\frac{x}{x+AB}=\frac{3}{5}$

$x=\frac{3AB}{2}$

Putting value of $x$ in Eq(1) we get

$\Rightarrow \frac{3AB}{2T}=\frac{3}{8}\times \frac{AB}{C}$

$\Rightarrow T:C=4:1$

Therefore Answer is $\left(B\right)$