CAT 2020 Quant Question [Slot 2] with Solution 19

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

1. 1:04
2. 7:05
3. 5:07
4. 4:01
Option: 3
Solution:

Given,

Let the speed of train 1 from A to B be s.

Then the speed of train 2 from A to B is 2s.

Time taken by train 1 to cover A to C =$\frac{D}{s} + \frac{{3D}}{{2s}} = \frac{{5D}}{{2s}}$

And, time taken by train 2 to cover A to C

$= \frac{D}{{2s}} + \frac{{3D}}{s} = \frac{{7D}}{{2s}}$

Required ratio $= \frac{{5D}}{{2s}}:\frac{{7D}}{{2s}} \Rightarrow 5:7$

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