Question : If the numerator of a fraction is increased by 140% and the denominator of the fraction is decreased by 20%, the resultant fraction is $\frac{12}{7}$. Find the original fraction.
Option 1: $\frac{4}{9}$
Option 2: $\frac{4}{7}$
Option 3: $\frac{7}{6}$
Option 4: $\frac{8}{9}$
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Correct Answer: $\frac{4}{7}$
Solution :
Let $\frac{x}{y}$ be the original fraction.
The fraction's numerator is increased by 140% and the denominator is decreased by 20%.
$\frac{x+1.4x}{y-0.2y} = \frac{12}{7}$
⇒$\frac{2.4x}{0.8y} = \frac{12}{7}$
⇒$\frac{3x}{y} = \frac{12}{7}$
⇒$\frac{x}{y} = \frac{12}{7\times 3}$
⇒$\frac{x}{y} = \frac{4}{7}$
Hence, the correct answer is $\frac{4}{7}$.
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