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Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t₁. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t₂. The time taken by her to walk up on the moving escalator will be:

1. t₁t₂ / (t₂ - t₁)
2. t₁t₂ / (t₂ + t₁)
3. t₁ - t₂
4. (t₁ + t₂) / 2

Correct answer: t₁t₂ / (t₂ + t₁)

Solution

If the escalator is stationary, Preeti’s walking speed is the whole distance divided by t₁. If she stands still on the moving escalator, the escalator’s speed is the whole distance divided by t₂. When both act together, the speeds add, so the total speed is D/t₁ + D/t₂. The time is distance divided by this sum, giving t₁t₂/(t₁+t₂).

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