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Question:

The distance from B to C is thrice that from A to B. Two trains travel from A to C via B. The speed of train 2 is double that of train 1 while traveling from A to B and their speeds are interchanged while traveling from B to C. The ratio of the time taken by train 1 to that taken by train 2 in travelling from A to C is

Explanation:

Let the distance from A to B = d and that from B to C = 3d.

Speed of train T₁ = s from A to B and 2s from B to C.

Total time taken by T₁ = $\frac{d}{s} + \frac{3 d}{2 s} = \frac{5 d}{2 s}$

Speed of train T₂ = 2s from A to B and s from B to C.

Total time taken by T₂ = $\frac{d}{2 s} + \frac{3 d}{s} = \frac{7 d}{2 s}$

∴ Ratio of time taken by T₁ and T₂ = $\frac{5 d}{2 s} : \frac{7 d}{2 s}$ = 5 : 7

Hence, option (c).

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