A man while travelling a distance of 200 km by a car at a speed of 40 km/hr, his car breaks down at half the journey and the remaining distance is covered by bus to reach his destination. If the total time taken to reach the destination is 4.5 hours, then find the speed of the bus

Correct option is A

​$$\text{Let the total distance be } 200 \text{ km.} \\[5pt]\text{The car breaks down at half the journey, so the car travels } 100 \text{ km.} \\[5pt]\text{The speed of the car is } 40 \text{ km/hr.} \\[10pt]\text{The time taken by the car to travel 100 km is:} \\\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{100}{40} = 2.5 \text{ hours} \\[10pt]\text{The remaining distance is also } 100 \text{ km. The total time taken to reach the destination is } 4.5 \text{ hours.} \\[5pt]\text{The time taken by the bus is:} \\\text{Time (bus)} = \text{Total time} - \text{Time (car)} = 4.5 - 2.5 = 2 \text{ hours} \\[10pt]\text{The distance travelled by the bus is } 100 \text{ km.} \\\text{Speed of the bus} = \frac{\text{Distance}}{\text{Time}} = \frac{100}{2} = 50 \text{ km/hr} \\[10pt]\text{Therefore, the speed of the bus is } 50 \text{ km/hr.}$$​​