Meeting of Motorbike and Car

CAT 2017 Slot 2 · QA · Medium · Speed, Time and Distance

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A motorbike leaves point A at 1 pm and moves towards point B at a uniform speed. A car leaves point B at 2 pm and moves towards point A at a uniform speed which is double that of the motorbike. They meet at 3:40 pm at a point which is 168 km away from A. What is the distance, in km, between A and B?

  1. A.

    364

  2. B.

    378

  3. C.

    380

  4. D.

    388

Answer

B

Explanation

Motorbike leaves A at 1 pm and meets at 3:40 pm   ⟹  \implies travelled for 2 hours 40 minutes = 83\frac{8}{3} hours.

Distance travelled by motorbike from A = 168 km. Speed of motorbike = 168/(8/3)=63168 / (8/3) = 63 km/h.

Speed of car = 2×63=1262 \times 63 = 126 km/h.

Car leaves B at 2 pm and meets at 3:40 pm   ⟹  \implies travelled for 1 hour 40 minutes = 53\frac{5}{3} hours.

Distance travelled by car from B = 126×53=210126 \times \frac{5}{3} = 210 km.

Total distance between A and B = 168+210=378168 + 210 = 378 km.

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