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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 ?

1. 364
2. 378
3. 380
4. 388

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Speed Time Distance

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 ?"

Hence, the answer is 378

Choice B is the correct answer

 

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