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
B
16
C
36
D
81

Solution

## The correct option is C 36Let 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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