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Raja observes that the angle of elevation
of the first floor of a building at a point $A$ on the ground is
30°. He moves $\sqrt{3}$ units towards the building to the point
$B$ and finds that the angle of elevation of the second floor of
the building is 60°. If each floor has the same height, height
of the 7th floor from the ground in units is

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answer is C.

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Detailed Solution

Let the height of each floor be $x$ units

$\begin{array}{l} \sqrt{3} = A B = O A - O B \\ = x \cot 30^{\circ} - 2 x \cot 60^{\circ} \\ = x \sqrt{3} - \frac{2 x}{\sqrt{3}} \end{array}$

$\Rightarrow x = 3$ and hence the required height is 21 units.

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