Correct Answer - Option 1 : 52 km/h

**Given:**

Total distance travelled = 78km

Time = 3 hours 30 minutes = 3 + 30/60 = 7/2 hours

**Formula:**

Speed = Distance/time

**Calculation:**

Let speed of Vaibhav and speed of Vignesh be a kmph and (91 - a) kmph respectively.

⇒ 78/a + 78/(91 - a) = 7/2

⇒ 7098 - 78a + 78a = 7/2 × (91a - a^{2})

⇒ a^{2} - 91a + 2028 = 0

⇒ a2 - 52a - 39a + 2028 = 0

⇒ a(a - 52) - 39(a - 52) = 0

⇒ (a - 52)(a - 39) = 0

a = 52 or a = 39

Vaibhav's speed is more than Vignesh, so a = 52kmph

**∴ Speed of Vaibhav is 52kmph.**