A bus passes two persons moving in the direction of the moving bus at a speed of 3 km/hr and 5 km/hr, respectively. The bus passes the first person in 10 s and the second person in 11 s. Find the speed of the bus.

25 km/hr

The correct answer is Option (3) → 25 km/hr

Let the speed of the bus = v km/hr and length of the bus = L.

Case 1: Passing first person (speed = 3 km/hr)

Relative speed = $v – 3$

Time = 10 s = $\frac{10}{3600}$​ hr

$L = (v - 3)\times \frac{10}{3600}$

Case 2: Passing second person (speed = 5 km/hr)

Relative speed = $v – 5$

Time = 11 s = $\frac{11}{3600}$​ hr

$L = (v - 5)\times \frac{11}{3600}$

Since both expressions equal the bus length L:

$(v - 3)\times 10 = (v - 5)\times 11$

$10v - 30 = 11v – 55$

$v = 25$

Speed of the bus = 25 km/hr