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Question 12 : 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 ?

- 364
- 378
- 380
- 388

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Given that motorbike leaves point A at 1 pm and moves towards point B.

Car leaves at point B at 2 pm and moves towards point A where the speed is equal to double that of motor bike.

Both meet at 3.40 pm at a point which is 168 km away from A

Bike travelled from 1 to 3:40 pm = \\frac{8}{3}) hrs at a speed of x

Car travelled from 2 to 3:40 pm = \\frac{5}{3}) hrs at a speed of 2x

\\frac{8}{3}) × x = 168

\\frac{5}{3}) × 2x = ?

This is in the ratio 8 : 10 = 168 : ?

⟹ 4 : 5 = 168 : ?

⟹ \\frac{168 × 5}{8}) = 210

A : B = 4 : 5 = 168 : 210

The distance, in km, between A and B is 168 + 210 = 378 kms

The question is **"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 ?" **

Choice B is the correct answer

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