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SSC CPO 2020 PYQ — Question 121

SSC CPO - 25 Nov 2020 - Shift 2 • Quantitative Aptitude • Q121

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Let A and B be two towers with the same base. From the midpoint of the line joining their feet, the angles of elevation of the tops of A and B are 30° and 45°, respectively. The ratio of the heights of A and B is :

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Correct answer: D

Explanation

The correct answer is Option 4 i.e. 1 : √3.

We know that,

tanθ = P/B

here, P = Perpendicular, B = Base

Now according to the question

In AOC

tan 30 = AC/OC

⇒ 131\over \sqrt3 = ACOCAC\over OC.........(1)

In BOD

tan 45 = BD/OD

⇒ 31\sqrt3\over1 = BDODBD \over OD .........(2)

Required ratio = 

⇒ 13×31\over {\sqrt3\times \sqrt3} = ACBDAC\over BD

⇒ 131\over3 = ACBDAC\over BD

Thus, The ratio of the heights of A and B = 1 : 3