A vertical stick 30 m long casts a shadow 15 m long on the ground. At the same time, a tower casts a shadow 75 m long on the ground. The height of the tower is :

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150 m

100 m

25 m

200 m

answer is A.

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Detailed Solution

Given, a vertical stick 30 m long casts a shadow 15 m long on the ground.
Shadow of a tower 75 m long.
Question Image

We have to find the height of the tower.
By AAA similarity criterion

, △ EBF ~ △ ABC .

∴ \frac{AB}{BC} = \frac{EB}{BF}

[corresponding sides of similar triangle are proportional]

\Rightarrow \frac{x + 30}{75} = \frac{30}{15}

\Rightarrow \frac{x + 30}{75} = 2

\Rightarrow x + 30 = 150

\Rightarrow h = 150 m

[since h = x+30]
Hence, the height of the tower is 150m.
Therefore, option 1 is correct.

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