An electric pole, 14 metres high, casts a shadow of 10 metres. The height of a tower that casts a shadow of 300 metres under similar conditions is: (in metres)

140

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480

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420

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280

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Solution

The correct option is C
420

Let h denote the height of an object and s the length of the shadow.
Let the height of the tower be x metres.

Note that more the height of an object, the more would be the length of its shadow.

Hence, this is a case of direct proportion. That is,
$\frac{h_{1}}{s_{1}}$ = $\frac{h_{2}}{s_{2}}$
$\frac{14}{10}$ = $\frac{x}{300}$

x = 420 metres

Hence the height of the tower = 420 metres

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