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 nterchanged 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

• A. 1: 4
• B. 7: 5
• C. 5:7
• D. 4:1

Answer 1

The Correct Option is C

Let the speed of Train 1 from point A to B be \(s\).
Then the speed of Train 2 from A to B is \(2s\).

Time taken by Train 1 to travel from A to C:
\[ \frac{D}{s} + \frac{3D}{2s} = \frac{5D}{2s} \]

Time taken by Train 2 to travel from A to C:
\[ \frac{D}{2s} + \frac{3D}{s} = \frac{7D}{2s} \]

The ratio of time taken (Train 1 : Train 2) is:
\[ \frac{5D}{2s} : \frac{7D}{2s} = 5 : 7 \]

✅ Final Answer: Option (C): \(5 : 7\)