Question : X is directly proportional to the square of Y. When X is 12, then Y is 2. Find the value of X when Y is 3.
Option 1: 30
Option 2: 9
Option 3: 27
Option 4: 18
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Correct Answer: 27
Solution :
$X\propto Y^2⇒ X = kY^2$
⇒ $\frac{\mathrm{X{_1}}}{\mathrm{Y^2{_1}}} = \frac{\mathrm{X{_2}}}{\mathrm{Y^2{_2}}} $
⇒ $\frac{12}{2^2} = \frac{\mathrm{X{_2}}}{3^2}$
⇒ $\mathrm{X{_2}} = \frac{12}{4}\times 9$
⇒ $\mathrm{X{_2}} = 27$
Hence, the correct answer is 27.
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