A bus is travelling with $$\frac{7}{8}$$​ of its actual speed to cover 42 km in 1 h 16 min. Find the actual speed of the bus.

Correct option is C

Given:

The bus is traveling at $$\frac{7}{8}$$​ of its actual speed.

Distance covered = 42 km

Time taken = 1 hour 16 minutes = 1 + $$\frac{16}{60} = \frac{76}{60}$$ hours

Formula Used:

Speed is calculated using the formula:

​$$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$$​

Since the bus is traveling at $$\frac{7}{8}$$​ of its actual speed, we can use this ratio to determine the actual speed.

Solution:

$$\text{Observed Speed} = \frac{42}{\frac{76}{60}} = \frac{42 \times 60}{76} = \frac{2520}{76} = 33.16 \text{ km/h} \\ \ \\\text{Actual Speed} = \frac{33.16 \times 8}{7} = \frac{265.28}{7} = 38 \text{ km/h}$$​