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 $8\frac{2}{5}$ hours and $4\frac{2}{7}$ 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?

• A. 84
• B. 56
• C. 63
• D. 70

Answer 1

Answer:

D. 70

Solution:

Given:

After passing each other, X and Y take $8\frac{2}{5}and4\frac{2}{7}hours$

The speed of X is 50 km/h

Concept Used:

If two trains start at the same time with speeds x km/h and y km/h and after meeting they reach their destination in t₁ hours and t₂ hours then the relation between speed and time is $\frac{x}{y}=\sqrt{\frac{t2}{t1}}$

Calculation:

Here x = 50 km/h

$t1=8\frac{2}{5}=\frac{42}{5}hours$

$t2=4\frac{2}{7}=\frac{30}{7}hours$

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

Accordingly,

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

${{50} \over a} = {\sqrt{{30 \times 5} \over {7 \times 42}}}$

${50 \over a} = \sqrt {5 \times 5 \over 7 \times 7}$

$\frac{50}{a}=\frac{5}{7}$

⇒ a = 70

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