A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is `30^0` . After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is`60^0` . Then the time taken (in minutes) by him, from B to reach the pillar, is : (1) 6 (2) 10 (3) 20 (4) 5

Options

A. 6
B. 10
C. 20
D. 5

Answer

D

Explanation

According to given information, we have the following figure.
Now, from `DeltaACD` and `DeltaBCD`, we have

`tan30^(@) = (h)/(x+y)`
and `tan60^(@)=(h)/(y)`
`implies h=(x+y)/(sqrt(3))" ...(i)"`
and `h=sqrt(3)y" ...(ii)"`
From Eqs. (i) and (ii), `(x+y)/(sqrt(3))=sqrt(3)y`
`implies x+y=3y`
`implies x-2y=0`
`implies y = (x)/(2)`
`because` Speed is uniform and distance x covered in 10 min.
`therefore` Distance `(x)/(2)` will be cover in 5 min.
`therefore` Distance y will be cover in 5 min.