A boy travelling at a speed of 15 km per hour reaches his school after 20 minutes. Next time he increases his speed by 5 km per hour but still he is 5 minutes late. What is the distance between his school and home?

Correct option is A

Given :

The boy walked at a speed of 15 kmph, reached school 20 minutes late.

When the speed was increased by 5 kmph, he was still 5 minutes late.

Formula Used:

$$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$$​Let the distance be x km.

Let us assume the correct time to reach school is 1 hour.

On converting the time 

$$20 \, \text{minutes} = \frac{20}{60} = \frac{1}{3} \, \text{hours}$$​

​$$5 \, \text{minutes} = \frac{5}{60} = \frac{1}{12} \, \text{hours}$$​​

For the first condition: 

​$$15 = \frac{x}{1 + \frac{1}{3}}$$​​

​$$15 = \frac{x}{\frac{4}{3}}$$​​

​$$x = 15 \times \frac{4}{3}$$​​

​$$x = 5 \times 4 = 20 \, \text{km}$$​