The denominator of a fraction is 3 more than its numerator. If the numerator is increased by 7 and denominator is decreased by 2, we obtain 2. The sum of numerator and denominator of the fraction is -
Correct Answer: 13
Let the numerator be n and the denominator be n + 3
$$\eqalign{ & {\text{According to question}} \cr & \frac{{n + 7}}{{\left( {n + 3} \right) - 2}} = \frac{2}{1} \cr & \frac{{n + 7}}{{n + 1}} = \frac{2}{1} \cr & 2n + 2 = n + 7 \cr & n = 5 \cr & {\text{Fraction = }}\frac{5}{{5 + 3}} = \frac{5}{8} \cr & {\text{Sum = 5 + 8 = 13}} \cr} $$
$$\eqalign{ & {\text{According to question}} \cr & \frac{{n + 7}}{{\left( {n + 3} \right) - 2}} = \frac{2}{1} \cr & \frac{{n + 7}}{{n + 1}} = \frac{2}{1} \cr & 2n + 2 = n + 7 \cr & n = 5 \cr & {\text{Fraction = }}\frac{5}{{5 + 3}} = \frac{5}{8} \cr & {\text{Sum = 5 + 8 = 13}} \cr} $$