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At a metro station, a girl walks up a stationary escalator in time t₁. If she remains stationary on the escalator, then the escalator take her up in time t₂. The time taken by her to walk up on the moving escalator will be

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$t_{1} t_{2} / (t_{2} + t_{1})$

$t_{1} - t_{2}$

$(t_{1} + t_{2}) / 2$

$t_{1} t_{2} / (t_{2} - t_{1})$

answer is C.

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Detailed Solution

Let the length of escalator be 'x'.

Speed of girl walking is $\frac{x}{t_{1}}$

Speed of the escalator is $\frac{x}{t_{2}}$

So the speed of girl walking on escalator will be $\frac{x}{t_{1}}$ + $\frac{x}{t_{2}}$ .

Time taken will be given by $T = \frac{x}{\frac{x}{t_{1}} + \frac{x}{t_{2}}} \Rightarrow \frac{t_{1} t_{2}}{t_{1} + t_{2}}$

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