Walking at 2/5 of his normal speed, Abhijeet is 48 minutes late in reaching his office. The usual time taken by him to cover the distance between his home and his office is:

Correct option is B

​Given:

Abhijeet is walking at $$\frac{2}{5}$$​ of his normal speed.

He is 48 minutes late in reaching his office.

Formula Used:

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

Solution:

Let the normal speed be S and the distance be D

Now, 

​$$\frac{5D}{2S} - \frac{D}{S} = 48$$​​

​$$\frac{5D}{2S} - \frac{2D}{2S} = 48$$​​

​$$\frac{3D}{2S} = 48$$​​

3D = 96S

D = 32S

Now, the usual time  = $$\frac{D}{S} = \frac{32S}{S}$$ = 32 minutes

Thus, the usual time taken by Abhijeet to reach his office is 32 minutes

Alternate Solution: ​

When distance is constant;

Speed $$\propto \frac{1}{time}$$

Speed changes  -     5         :    2 

so, time change -    2        :    5 

5 - 2 = 48 unit 

3 unit = 48 min.

then 2 unit = $$\frac{48}{3} \times 2$$​ = 32 min.