Question
Which number can replace both the question marks in the equation ?
$$\frac{{4\frac{1}{2}}}{?} = \frac{?}{{32}}$$
$$\frac{{4\frac{1}{2}}}{?} = \frac{?}{{32}}$$
Answer: Option D
$$\eqalign{
& {\text{Let,}} \cr
& {\text{ }}\frac{{4\frac{1}{2}}}{x} = \frac{x}{{32}} \cr
& {\text{Then,}} \cr
& \Leftrightarrow {x^2} = 32 \times \frac{9}{2} \cr
& \Leftrightarrow {x^2} = 144 \cr
& \Leftrightarrow x = \sqrt {144} \cr
& \Leftrightarrow x = 12 \cr} $$
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$$\eqalign{
& {\text{Let,}} \cr
& {\text{ }}\frac{{4\frac{1}{2}}}{x} = \frac{x}{{32}} \cr
& {\text{Then,}} \cr
& \Leftrightarrow {x^2} = 32 \times \frac{9}{2} \cr
& \Leftrightarrow {x^2} = 144 \cr
& \Leftrightarrow x = \sqrt {144} \cr
& \Leftrightarrow x = 12 \cr} $$
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