Correct Answer - Option 2 :

2 h 26 min 40 s

**Given: **

Speed of P = 50 km/h

Speed of Q = 40 km/h

Distance = 100 km

**Formula Used:**

Speed = Distance/Time

**Concept Used:**

If two objects are moving with speeds S_{1} and S_{2} in the opposite direction

Their relative speed is S_{1} + S_{2}

**Calculation:**

Time taken by P to reach the destination = 100/50 = 2 h

Q starts after 30 min, therefore, distance covered by Q in 1 h 30 min = 40 × 1.5 = 60 km

Now, A turns back.

Distance to be covered by both to meet = 100 – 60 = 40 km

Relative speed = 50 + 40 = 90 km/h

Time = 40/90 km = 4/9 × 60 min = 26 min 40 s

Total time taken by P = 2 h + 26 min 40 s

⇒ 2 h 26 min 40 s

**∴ ****P takes 2 h 26 min 40 s to meet Q.**