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

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 \(C\)
= \(\frac{D}{2s}+\frac{3D}{s}=\frac{7D}{s}\)
Required ratio = \(\frac{5D}{2s}:\frac{7D}{2s} ⇒ 5:7\)
So, the correct option is (C): \(5:7\)

Answer 2

Let's assume the distance from A to B be x, then the distance from B to C will be 3x.
So, the speed of Train 2 is double of Train 1. Let the speed of Train 1 be v, then the speed of Train 2 will be 2v while covering the distance from A to B.
Time taken by Train 1 = \(\frac{x}{v}\)
Time taken by Train 2 = \(\frac{x}{2v}\)
So, distance from B to C is 3x and speed of Train 2 is v.
Speed of Train 1 is 2v.
Now, we can calculate total time taken :
Total time taken by Train 1 = \(\frac{x}{v(1+\frac{3}{2})}=\frac{\frac{5}{2}}{\frac{x}{v}}\)
Total time taken by Train 2 = \(\frac{x}{v(3+\frac{1}{2})}=\frac{\frac{7}{2}}{\frac{x}{v}}\)
Therefore, the ratio of time taken :
\(=\frac{\frac{5}{2}}{\frac{7}{2}}=\frac{5}{7}\)
So, the correct option is (C) : 5 : 7.