SSC CGL 2022 PYQ — Question 64

The correct answer is option 3 i.e. 54 km/h

Given:

After meeting each other, time taken by P = 4 hours 48 minutes and

time taken by Q = 3 hours 20 minutes to reach stations T and S respectively

Speed of P = 45 km/h

Concept Used:

If two trains run with the speed of x km/hr and y km/hr and they reach their destination after meeting each other in t1 and t2 hours respectively, then

${({x \over y})^2} = {t2 \over t1}$     ...(i)

Explanation:

Let the speed of Q be x km/hr.

Using equation (i), we get

${({Speed of P \over Speed of Q })^2} = {3\ hours\ 20\ minutes \over 4\ hours\ 48\ minutes}$

Now, 3 hours 20 minutes = 10/3 hours

And 4 hours 48 minutes = 24/5 hours

⇒ ${({Speed\ of\ P \over Speed\ of\ Q})^2} = {{10 \over 3} \over {24 \over 5}}$

⇒ (45/x)² = 25/36

⇒ (45/x)² = (5/6)²

⇒ 45/x = 5/6

⇒ x = 54

Hence the speed of Q is 54 km/h.