A bus travelling with $$\frac57$$​ of its actual speed covers 42 km in 1 h 40 min 48 s. Find the actual speed of the bus.

Correct option is B

Given:

​$$\text{Time taken} = 1 \, hr \, 40 \, min \, 48 \, sec = 1 \, hr + \frac{40}{60} \, hr + \frac{48}{3600} \, hr = \frac{126}{75} \, hr \\\text{Distance travelled} = 42 \, km \\$$​​

Formula Used:

$$\text{Speed} = \frac{\text{distance}}{\text{time}}$$​​

Solution:

​$$\text{Time taken} = 1 \, hr \, 40 \, min \, 48 \, sec = 1 \, hr + \frac{40}{60} \, hr + \frac{48}{3600} \, hr = \frac{126}{75} \, hr \\\text{Distance travelled} = 42 \, km \\\text{Speed} = \frac{\text{distance}}{\text{time}} = \frac{42}{\frac{126}{75}} = \frac{42 \times 75}{126} \\\therefore \text{Speed of car} = \left(\frac{5}{7}\right) \times \text{actual speed} \\\Rightarrow \text{Actual speed} = \frac{42 \times 75}{126} \times \frac{7}{5} = 7 \times 5 = 35 \, km/hr$$​​