Ratio of speeds of cars

CAT 2018 Slot 2 · QA · Medium · Speed, Distance & Time

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Points A, P, Q and B lie on the same line such that P, Q and B are, respectively, 100 km, 200 km and 300 km away from A. Cars 1 and 2 leave A at the same time and move towards B. Simultaneously, car 3 leaves B and moves towards A. Car 3 meets Car 1 at Q, and Car 2 at P. If each car is moving in uniform speed then the ratio of the speed of Car 2 to that of Car 1 is

  1. A.

    1 : 4

  2. B.

    2 : 9

  3. C.

    1 : 2

  4. D.

    2 : 7

Answer

A

Explanation

Let the speeds of Car 1, Car 2, and Car 3 be v1,v2,v_1, v_2, and v3v_3 respectively.

Car 3 leaves B (300 km300\text{ km} from A) and moves towards A. Car 1 leaves A towards B. Car 3 meets Car 1 at Q (200 km200\text{ km} from A, 100 km100\text{ km} from B). In this time, Car 1 travels 200 km200\text{ km} and Car 3 travels 100 km100\text{ km}. Since time is the same, v1v3=200100=2  ⟹  v1=2v3\frac{v_1}{v_3} = \frac{200}{100} = 2 \implies v_1 = 2v_3.

Car 3 meets Car 2 at P (100 km100\text{ km} from A, 200 km200\text{ km} from B). In this time, Car 2 travels 100 km100\text{ km} and Car 3 travels 200 km200\text{ km}. Since time is the same, v2v3=100200=12  ⟹  v2=12v3\frac{v_2}{v_3} = \frac{100}{200} = \frac{1}{2} \implies v_2 = \frac{1}{2}v_3.

Thus, the ratio of the speed of Car 2 to Car 1 is: v2v1=12v32v3=14=1:4\frac{v_2}{v_1} = \frac{\frac{1}{2}v_3}{2v_3} = \frac{1}{4} = 1 : 4

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