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CAT 2017 [slot 2] Question with solution 12

Question 46:
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. 364
  2. 378
  3. 380
  4. 388
Option: 2
Explanation:

Let the distance traveled by the car be x KMs
Distance traveled by the bike = 168 KMs
Speed of car is double the speed of bike
=> $\frac{x}{3:40 - 2:00}$ = $2 \times \frac{168}{3:40 - 1:00}$
=> $\frac{x}{100}$ = $2 \times \frac{168}{160}$
=> x = 210
Hence the distance between A and B is x + 168 = 378 KMs

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