# TANCET 2013 Quant Qn 45: Number Properties

## Question

Easy Quantitative Reasoning

There are 35 steps in a temple. By the time Chithra comes down two steps, Madhu goes up one step. If they start simultaneously and keep their speed uniform, then at which step from the bottom will they meet?

1. 9th step
2. 12th step
3. 13th step
4. 8th step
5. None of the above

Correct Answer    Choice (2). 12th step

## Explanatory Answer - step by step

1. Let time taken by Chithra to climb down 2 steps = 1 second.
2. In the same time, i.e., 1 second Madhu would climb up 1 step
3. In one second, distance covered by the two of them together = 2 + 1 = 3 steps.
4. The two of them will meet when they have covered the gap of 35 steps between them.
5. In 11 seconds, total steps covered will be 11 * 3 = 33 steps.
6. i.e. Madhu will cover 11 steps from the bottom and Chithra will cover 22 steps from the top.
7. Number of steps yet to cover before they meet = 35 - 33 = 2 steps
8. During the 12th second, Madhu and Chithra will meet.
9. Madhu will climb one step to reach the 12th. So, they will meet at the 12 step from the bottom.

The correct answer is Choice (2). 12th step from the bottom.

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