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Relative speed for simultaneous meeting

CAT 2023 Slot 2 · Quantitative Ability · Medium · Arithmetic

This is a medium Quantitative Ability question from the CAT 2023 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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Ravi is driving at a speed of 40 km/h on a road. Vijay is 54 meters behind Ravi and driving in the same direction as Ravi. Ashok is driving along the same road from the opposite direction at a speed of 50 km/h and is 225 meters away from Ravi. The speed, in km/h, at which Vijay should drive so that all the three cross each other at the same time, is

  1. A.

    58.8

  2. B.

    64.4

  3. C.

    67.2

  4. D.

    61.6

Answer

D

Explanation

Ravi's speed = 4040 km/h. Ashok's speed = 5050 km/h (opposite direction). Relative speed of Ravi and Ashok = 40+50=9040 + 50 = 90 km/h =90×518=25= 90 \times \frac{5}{18} = 25 m/s.

Distance between Ravi and Ashok = 225225 meters. Time taken for Ravi and Ashok to meet =22525=9= \frac{225}{25} = 9 seconds.

In 9 seconds, Ravi travels =40×518×9=100= 40 \times \frac{5}{18} \times 9 = 100 meters.

Since Vijay starts 54 meters behind Ravi, Vijay must travel 100+54=154100 + 54 = 154 meters in 9 seconds to meet them at the exact same time.

Vijay's speed =1549= \frac{154}{9} m/s =1549×185=3085=61.6= \frac{154}{9} \times \frac{18}{5} = \frac{308}{5} = 61.6 km/h.

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