Two friends start at the same time from cities P and Q towards cities Q and P respectively. After meeting at some point between P and Q, they reach their destinations in 54 and 24 minutes respectively. In what time did the one who moved from Q to P complete his journey?

Correct option is C

Let the time taken to meet be t minutes.
Let the speeds of that friend who started from P and who started form Q be S1 and S2 respectively.
We know,
​$$\frac{S1}{S2} = \sqrt{\frac{t1}{t2}} \\ \ \\\frac{S1}{S2} = \sqrt{\frac{24}{54}} \\ \ \\\frac{S1}{S2} = \frac{2}{3}$$​​
Distance covered by the first friend in (t + 54) minutes = Distance covered by the second friend in (t + 24) minutes
Since they meet at the same point, their distance covered is equal.
S1 × (t + 54) = S2 × (t + 24)
​$$\frac{S1}{S2} = \frac{t+24}{t+54}$$​​
2t + 108 = 3t + 72
t = 36 minutes
So, one who move Q to P  covers the distance in 36 + 24 = 60 minute.