Question : If the numerator of a fraction is increased by 60% and the denominator is increased by 40%, then the resultant fraction is $\frac{16}{63}$. The original fraction is:
Option 1: $\frac{5}{9}$
Option 2: $\frac{2}{9}$
Option 3: $\frac{2}{11}$
Option 4: $\frac{4}{9}$
Correct Answer: $\frac{2}{9}$
Solution :
If the numerator of a fraction is increased by 60% and the denominator is increased by 40%, then the resultant fraction is $\frac{16}{63}$. The original fraction is:
The numerator increased by 60%
The denominator increased by 40%
Resultant fraction = $\frac{16}{63}$
Calculation:
Let the original fraction be $\frac{x}{y}$
According to the question
60% of numerator = $0.6x$
40% of denominator = $0.4y$
⇒ New fraction = $\frac{x + 0.6x}{y + 0.4y} $ = $\frac{1.6x}{1.4y} $
⇒ $\frac{16}{63} = \frac{16x}{14y}$
⇒ $\frac{14}{63} = \frac{x}{y}$
⇒ $\frac{2}{9} = \frac{x}{y}$
$\therefore$ The original fraction is $\frac{2}{9}$
Hence, the correct answer is $\frac{2}{9}$.
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