A student goes to his college from his hostel at the speed of 4 km/h and returns at the speed of 3 km/h. If he takes 7 hr in going and coming, the distance between his college and hostel is:

Correct option is A

Given:

A student goes to his college from his hostel at the speed of 4 km/h and returns at the speed of 3 km/h.

If he takes 7 hr in going and coming.

Formula Used:

Distance = Speed $$\times$$​ Time 

Solution:

Let the distance between the college and hostel be D.

The time taken to travel from the hostel to the college at 4 km/h = $$\frac{D}{4}$$

The time taken to return from the college to the hostel at 3 km/h = $$\frac{D}{3}$$

The total time,

$$\frac{D}{4} + \frac{D}{3} = 7$$

​​​​$$\frac{3D+4D}{12} = 7$$

​$$\frac{7D}{12} = 7$$​​

7D = 84

D = $$\frac{84}{7}$$​​

D = 12

So, the distance between the college and hostel is 12 km.

Thus, the correct answer is (a).

Alternative Method:

When distance constant then speed and time ratio reverse,

Speed → 4x : 3x

Time → 3x : 4x

7x = 7

x = 1

Time = 3x = 3 $$\times$$ 1 = 3

Distance = 3 $$\times$$​ 4 = 12 km