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A 21-meter-long shadow is cast by a water tank. A 9.5 m tall tree simultaneously throws an 8 m long shadow. The shadows' lengths are directly proportional to their heights. Find the tank's height.

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23.5 m

24.9 m

32.5 m

33.6 m

answer is B.

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Detailed Solution

Given that, the water tank's length is 21 m.
The tree is 9.5 metres tall.
An 8 m-long shadow is cast by a tree.
We know that if two quantities

x

and

y

vary in the same way while maintaining a constant ratio between their respective values, then the two quantities are said to be in direct proportion.
i.e.

x y = k,

where k is a constant positive number.
Given, the length of the water tank is 21 m long.
Let’s assume that the height of tank is

x .

Since the shadows' lengths are directly proportional to their heights, therefore we have

8 9.5 = 21 x ⇒ x = 21 × 9.5 8 ⇒ x = 199.5 8 ⇒ x = 24.9 m

Hence, the tank's height is 24.9 m.
Thus, option (2) is correct.

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