​Suppose there is a fraction whose numerator as well as denominator both are positive integers. If the numerator is increased by 20% and the denominator is decreased by 20% its value becomes$$\frac{6}{9}$$ what is the fraction?​​

Correct option is D

Given:

​$$\text{Original fraction } \frac{x}{y} \\\ \\\text{New fraction } = \frac{1.2x}{0.8y} = \frac{6}{9} = \frac{2}{3} \\$$

$$\textbf{Solution:} \\\quad \frac{1.2x}{0.8y} = \frac{2}{3} \\\ \\\quad 3.6x = 1.6y \\\ \\\quad \frac{3.6x}{0.4} = \frac{1.6y}{0.4} \Rightarrow 9x = 4y \\\ \\\quad \frac{x}{y} = \frac{4}{9} \\\ \\\textbf{Final Answer:} \\\quad \boxed{\frac{4}{9}}$$

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