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Speed Ratio After Crossing

CAT 2020 Slot 2 · Quantitative Ability · Easy · Arithmetic

This is an easy Quantitative Ability question from the CAT 2020 Slot 2 paper. It tests Arithmetic. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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A and B are two points on a straight line. Ram runs from A to B while Rahim runs from B to A. After crossing each other, Ram and Rahim reach their destinations in one minute and four minutes, respectively. If they start at the same time, then the ratio of Ram's speed to Rahim's speed is

  1. A.

    2

  2. B.

    2\sqrt{2}

  3. C.

    \sqrt{2}

  4. D.

    \frac{1}{2}

Answer

A

Explanation

When two objects start at the same time from two points and move towards each other, the ratio of their speeds is given by: v1v2=t2t1\frac{v_1}{v_2} = \sqrt{\frac{t_2}{t_1}} where t1t_1 and t2t_2 are the times taken to reach destination after crossing each other. Here t1=1 mint_1 = 1\text{ min} and t2=4 mint_2 = 4\text{ min}. vRamvRahim=41=2\frac{v_{\text{Ram}}}{v_{\text{Rahim}}} = \sqrt{\frac{4}{1}} = 2

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