Two trains P and Q start from stations S and T towards each other. Train P takes 4 hours 48 minutes and train Q takes 3 hours 20 minutes to reach T and S, respectively, after they meet. If the speed of train P is 45 km/h, what is the speed of train Q?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 02 Dec 2022 Shift 4)

Answer 1

Given:

After meeting, trains P and Q complete their journey in 4 hours 48 minutes and 3 hours 20 minutes respectively

Speed of train P = 45 km/hr

Formula used:

After meeting each other, the time required by the trains to reach the destination

\(\frac{S_1}{S_2}\) = \(\sqrt{\frac{T_2}{T_1}} \)

Where, S₁ and S₂ are the speeds of trains, and T₁ and T₂ are the times taken by trains to reach the destination after meeting

Calculation:

4 hours 48 minutes = 24/5 hours

3 hours 20 minutes = 10/3 hours

According to the question,

\(\frac{45}{S_2}\) = \(\sqrt{\frac{(10/3)}{(24/5)}} \)

⇒ \(\frac{45}{S_2}\) = \(\sqrt{\frac{10×5}{24×3}} \)

⇒ \(\frac{45}{S_2}\) = \(\frac{5}{6}\)

⇒ S₂ = (45 × 6)/5 = 54

∴ The speed of Q is 54 km/hr.

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