Option 2 : 70. 23 seconds

**Concept:**

Speed = Distance/ Time

**Calculation: **

Length of train P = 350 m

Length of train Q = 440 m

Distance to be covered by both the trains = 350 m + 440 m ⇒ 790 m

Speed of train P in m/sec = 54 × 5/18 ⇒ 15 m/sec

Speed of train Q in m/sec = 108 × 5/18 ⇒ 30 m/sec

Relative speed of trains while moving in the same direction = 30 - 15 ⇒ 15 m/sec

Relative speed of trains while moving in the opposite direction = 15 + 30 ⇒ 45 m/sec

Time taken by both the trains to cross each other while moving in same direction = 790/15 ⇒ 52.67 seconds

Time taken by both the trains to cross each other while moving in opposite direction = 790/45 ⇒17.56 seconds

**∴ The required sum of the time = 52.67 seconds + 17.56 seconds ⇒ 70.23 seconds (approximately)**