Aman covers a certain distance between his house and his office on a scooter. At an average speed of 30 km/h, he is late by 10 min. However, at a speed of 40 km/h he reaches his office 5 min earlier. Find the distance between his house and his office.

Correct option is A

​Given:

Speed at 30 km/h: 10 minutes late.

Speed at 40 km/h: 5 minutes early. 

Formula Used:​

Speed = $$\frac{Distance}{time}$$​​

Solution:

Let the distance be d km and the time taken at the correct speed be t hours.

Time at 30 km/h: $$\frac{d}{30} hours.$$​​

Late by 10 minutes=>$$\text{Late by 10 minutes} \Rightarrow \frac{d}{30} = t + \frac{10}{60}$$​​

Time at 40 km/h:  $$\frac{d}{40} hours.$$​​

Early by 5 minutes=>$$\text{Early by 5 minutes} \Rightarrow \frac{d}{40} = t - \frac{5}{60}$$​​

Now, subtract the second equation from the first:

​$$\left( \frac{d}{30} - \frac{d}{40} \right) = \frac{10}{60} + \frac{5}{60} = \frac{15}{60} = \frac{1}{4}$$​​

​$$\frac{4d - 3d}{120} = \frac{1}{4}$$​ 

$$\frac{d}{120} = \frac{1}{4} \quad \Rightarrow \quad d = 30 \, \text{km}$$ 

Thus, the distance is 30 km.