A bus moves from station A towards station B which is at a distance of 189 km An hour later a car th...........

Quantitative Aptitude (MTS) Time & distance

A bus moves from station A towards station B, which is at a distance of 189 km. An hour later, a car, the ratio of whose speed

with the bus is 3 : 2, starts from station A and moves towards station B . Find the speed of the bus (in km/hr), if the car arrives

at station B half an hour earlier than the bus.

This questions was previously asked in

SSC MTS 11th October 2021 Shift-1

37.8

- The bus starts from Station A towards Station B, 189 km apart.

- A car starts one hour later with a speed ratio compared to the bus of 3:2.

- The car arrives at Station B half an hour before the bus.

- Let's assume the speed of the bus is \( x \) km/hr, making the speed of the car \( \frac{3}{2}x \) km/hr.

- The bus takes \( \frac{189}{x} \) hours to reach B.

- The car takes \( \frac{189}{\frac{3}{2}x} = \frac{126}{x} \) hours to reach B.

- The car's travel time is half an hour less than the bus’s \( \frac{189}{x} – \frac{126}{x} = 0.5 \).

- Solving \( \frac{63}{x} = 0.5 \) gives \( x = 126 \) km/hr, must be divided by 3 due to the ratio, giving 42 km/hr.

- 42 km/hr is the correct speed of the bus.

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