Question

Two trians X and Y start at the same time, X from station A to B and Y from B to A. After passing each other, X and Y take \(8\dfrac{2}{5}\) hours and \(4\dfrac{2}{7}\) hours, respectively, to reach their respective destinations. If the speed of X is 50 km/h, then what is the speed (in km/h) of Y?
1. 84
2. 56
3. 63
4. 70

Answer 1

Correct Answer - Option 4 : 70

Given:

After passing each other, X and Y take \(8\dfrac{2}{5}\) hours and \(4\dfrac{2}{7}\) hours

The speed of X is 50 km/h

Concept Used:

If two trains start at the same time with speed x km/h and y km/h and after meeting they reached their destination in t₁ hours and t₂ hours then the relation between speed and time is \({x \over y} = \sqrt {t_2 \over t_1}\)

Calculation:

Here x = 50 km/h

t₁ = \(8{2 \over 5}\) hours = 42/5 hours

t₂ = \(4{2 \over 7}\) hours = 30/7 hours

Let, the speed of the train Y be a km/h

Accordingly,

\({50 \over a} = {\sqrt{{30 \over 7} \over {42 \over 5}}}\)

⇒ \({{50} \over a} = {\sqrt{{30 \times 5} \over {7 \times 42}}}\)

⇒ \({50 \over a} = \sqrt {5 \times 5 \over 7 \times 7}\)

⇒ 50/a = 5/7

⇒ a = 70

∴ The speed of the train Y is 70 km/hr.