P can complete a round of circular track in 1 minute and 30 seconds while Q can complete a round in 45 seconds. If they start moving from the same point and move in opposite directions, then they meet after _____ seconds.

Correct option is C

Given:
Time taken by P to complete 1 round = 1 minute 30 seconds = 90 seconds
Time taken by Q to complete 1 round = 45 seconds
Formula Used:
Time to meet when moving in opposite directions = $$\frac{{PQ}}{{P + Q}}$$​ , where P and Q are time taken for one round
Solution:
Let the length of the circular track be L units.
Speed of P = $$\frac{L}{90}$$​ units/sec

Speed of Q = $$\frac{L}{45}$$​ units/sec
Relative speed when moving in opposite directions = $$\frac{L}{90} + \frac{L}{45} = \left(\frac{1}{90} + \frac{1}{45}\right)L = \frac{1 + 2}{90}L = \frac{3L}{90} = \frac{L}{30}$$​​
Time to meet = Distance / Relative speed = $$\frac{L}{\frac{L}{30}} = 30 \text{ seconds}$$​​
Therefore, they will meet after 30 seconds.

Exam Hall Method: