If a bus covers 195 km in 3 hours and a train covers 300 km in 4 hours, then find the ratio of their speeds.

Given, a bus covers 195 km in 3 hours and a train covers 300 km in 4 hours.

For bus:

Distance covered by the bus in 3 hours = 195 km.

→ Distance covered by the bus in 1 hour = $\frac{195}{3} =\mathbf{ }\mathbf{65}\mathbf{ }\mathbf{km}\mathbf{.}$

Thus, the speed of the bus is 65 km/hr.

For train:

Distance covered by the train in 4 hours = 300 km.

→ Distance covered by the train in 1 hour = $\frac{300}{4} =\mathbf{ }\mathbf{75}\mathbf{ }\mathbf{km}\mathbf{.}$

Thus, the speed of the train is 75 km/hr.

Now, the required ratio:

$\Rightarrow \frac{\mathrm{Speed} \mathrm{of} \mathrm{bus}}{\mathrm{Speed} \mathrm{of} \mathrm{train}}=\frac{65 \mathrm{km}/\mathrm{hr}.}{75 \mathrm{km}/\mathrm{hr}.}$

$\Rightarrow \frac{\mathrm{Speed} \mathrm{of} \mathrm{bus}}{\mathrm{Speed} \mathrm{of} \mathrm{train}}=\frac{\mathbf{13}}{\mathbf{15}}$

Hence, the required ratio of their speeds is 13: 15.