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 spee

Question

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.

FirstInTest · Accepted Answer

Correct answer: C. Let the speed of the bus be $v$ km/hr.
Convert speeds to m/s: $1 	ext{ km/hr} = 5/18 	ext{ m/s}$.
Bus speed = $v 	imes 5/18$ m/s.
Person 1 speed = $3 	imes 5/18$ m/s.
Person 2 speed = $5 	imes 5/18$ m/s.

Let L be the length of the bus.
When a bus passes a person, the distance covered is the length of the bus.
Relative speed = (Speed of bus - Speed of person) since they are moving in the same direction.
Time = Distance / Relative Speed.

Case 1: Bus passes Person 1 (speed 3 km/hr) in 10 s.
Relative speed = $(v - 3) 	imes 5/18$ m/s.
$10 = L / ((v - 3) 	imes 5/18)$
$L = 10 	imes (v - 3) 	imes 5/18$

Case 2: Bus passes Person 2 (speed 5 km/hr) in 11 s.
Relative speed = $(v - 5) 	imes 5/18$ m/s.
$11 = L / ((v - 5) 	imes 5/18)$
$L = 11 	imes (v - 5) 	imes 5/18$

Equate the expressions for L:
$10 	imes (v - 3) 	imes 5/18 = 11 	imes (v - 5) 	imes 5/18$
Cancel $5/18$ from both sides:
$10(v - 3) = 11(v - 5)$
$10v - 30 = 11v - 55$
$55 - 30 = 11v - 10v$
$25 = v$

The speed of the bus is 25 km/hr.

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