Walking at $$\frac{7}{8}$$​ of its usual speed a bus is 10 minutes too late. Find its usual time to cover the journey?

Correct option is B

Given:

The bus is 10 minutes late when walking at $$\frac{7}{8}$$​ of its usual speed.

We need to find the usual time taken by the bus to cover the journey.

Concept Used:

The relationship between speed, distance, and time is given by:

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

Solution:

Let the usual time to cover the journey be t minutes.

When the bus walks at $$\frac{7}{8}$$​ of its usual speed, it will take longer to cover the same distance.

The time taken in this case is $$\frac{8}{7}$$​ times the usual time because speed and time are inversely proportional for the same distance.

The new time taken to cover the journey is:

​$$\text{New time} = \frac{8}{7} \times t$$​

The problem states that the bus is 10 minutes too late, so the new time is 10 minutes more than the usual time:

​$$\frac{8}{7} \times t = t + 10$$​

​$$\frac{8}{7} \times t - t = 10$$​

​$$\left( \frac{8}{7} - 1 \right) t = 10$$​

​$$\frac{1}{7} \times t = 10$$​

t=10×7=70

The usual time to cover the journey is 70 minutes.