Question

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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 at exactly the exit. What is the ratio of the speed of the train to that of the cat?

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Answer 1

$\huge\tt\color{darkblue}{\fbox{\tt{αηѕωєя}}}$

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.

$\sf\red{\underline{When\: The\: cat\: moves \:Towards \:the\: Entrance:}}$

$\Rightarrow$ $\frac{x}{T}$ = $\frac{3}{8} \times \frac{AB}{C}$ ------------ (i)

$\sf\red{\underline{When \:cat \:moves\: towards \:the \:exit :}}$

$\Rightarrow$ $\frac{x+AB}{T}$ = $\frac{5}{8} \times \frac{AB}{C}$ -------------- (ii)

$\sf\red{\underline{Divide\: (i) \: by (ii) :}}$

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

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

$\sf\red{\underline{Substitute\: the\: value \:of \:x \:in\: Eq(i)......}}$

We get,

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

$\Rightarrow$ T:C = 4:1

$\therefore$ The ratio of the speed of the train to that of the cat is 4:1.

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