A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 60° and when he retires 40 metres away from the tree, the angle of elevation becomes 30°. The breadth of the river is

As per the given question,

Let C be the point where the man is and D be the point when retires 40m. Let AB be the length of the tree.

We need to find the breadth of river that is 'BC' 

From triangle ABD,

Tan 30$$^{\circ}$$ = $$\frac{AB}{40 + x}$$

$$\frac{1}{\sqrt{3}} = \frac{AB}{40 + x}$$

AB = $$\frac{40 + x}{\sqrt{3}}$$ ......(1)

From triangle ABC,

Tan 60$$^{\circ} = \frac{AB}{x}$$

$$\sqrt{3} = \frac{AB}{x}$$

AB = $$\sqrt{3}x$$ ..................(2)

From equations (1) and (2)

$$\frac{40 + x}{\sqrt{3}}$$ = $$\sqrt{3}x$$

40 + x = 3x 

x = 20 m

Hence, option B is the correct answer.