The numerator and denominator of a fraction are in the ratio 3 : 4. If 9 is subt

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The numerator and denominator of a fraction are in the ratio 3 : 4. If 9 is subtracted from the numerator, the resulting fraction in $$\frac{2}{3}$$ of the original fraction. The numerator of the original fraction is

Options:

A . 27

B . 18

C . 36

D . 9

Answer: Option A
$$\eqalign{
& {\text{Let}}\,{\text{the}}\,{\text{fraction}}\,{\text{be}}\,\frac{{3k}}{{4k}} \cr
& \therefore \frac{{ {3k - 9} }}{{4k}} = {\frac{2}{3}} \cr
& \therefore 9k - 27 = 8k \cr
& \therefore k = 27 \cr } $$

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