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.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 25 km/hr
When the bus overtakes a person walking the same way, it gains on him only at the relative speed, bus speed minus the person’s speed, and to pass him it must gain its own length. The bus length is the same in both cases, so the two distances can be equated.
The speeds:
Speed of the bus \(=v\) km/h
Relative speeds \(v-3\) and \(v-5\) km/h
The bus length (the same unit conversion applies to both sides, so it cancels):
Length of the bus \(=(v-3)\times10\,\mathrm{s}=(v-5)\times11\,\mathrm{s}\)
\(10v-30=11v-55\), so \(v=25\) km/h