Question

If the numerator and the denominator of a fraction is decreased by 2, then the resulting fraction is $\frac{1}{2}$. If in case the numerator is increased by 2 and the denominator by 1, then the result is 1. The sum of the numerator and the denominator is ___.

• A. 7
• B. 3
• C. 4
• D. -7

Answer 1

The correct option is A 7

Let the fraction be $\frac{x}{y}$ (.i.e., $x$ be the numerator and y be the denominator of the fraction).
Then, by question, we have $\frac{x-2}{y-2}=\frac{1}{2}$ and $\frac{x+2}{y+1}=1$.
On rearrangement, we have $2x-y=2...\left(1\right)$
$x-y=-1...\left(2\right)$
Solving by the method of substitution,
(2)$⟹x=y-1$
Substituting this value of $x$ in (1) and solving for $y$, $2(y-1)-y=2⟹y=4$
$⟹x=y-1=4-1=3$
Thus, the fraction is $\frac{3}{4}$.
$⟹x+y=3+4=7$