Question

The sum of numerator and denominator of a fraction is 8. If 2 is added to numerator and 3 is subtracted from denominator, the fraction becomes $\frac{5}{2}$, find the original fraction.

• A. $\frac{1}{5}$
• B. $\frac{3}{5}$
• C. $\frac{1}{2}$
• D. $\frac{5}{3}$

Answer 1

The correct option is B $\frac{3}{5}$

Let the numerator of the original fraction = x
Sum of the numerator and denominator = 8
So, denominator of the original fraction = 8 - x
According to question,
$\frac{x+2}{8-x-3}$ = $\frac{5}{2}$
$\frac{x+2}{5-x}$ = $\frac{5}{2}$
2x + 4 = 25 - 5x
7x = 21
x = 3
So, denominator = 8 - 3 = 5
Hence, the original fraction is $\frac{3}{5}$.
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