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Question

The number that should be added to both the numerator and denominator of $$\displaystyle \frac{4^{2}}{9^{2}}$$ so that the fraction becomes $$\displaystyle \frac{4}{9}$$ is


A
0
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B
16
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C
36
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D
81
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Solution

The correct option is C 36
Let the number to be added be x Then
$$\displaystyle \frac{4^{4}+x}{9^{9}+x}=\frac{4}{9}\Rightarrow \frac{16+x}{81+x}=\frac{4}{9}$$
$$\displaystyle \Rightarrow 144+9x=324+4x$$
$$\displaystyle \Rightarrow 9x-4x=324+4x$$
$$\displaystyle \Rightarrow 9x-4x=324-144\Rightarrow 5x=180$$
$$\Rightarrow x=\dfrac{180}{5}=36$$

Mathematics

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