Subject: General Aptitude · Chapter: Problems on Numbers · Exam: · Marks: · Difficulty:
The sum of the numerator and denominator of a fraction is 11 . If 1 is added to the numerator and 2 is subtracted from the denominator, it becomes $\frac{2}{3}$. The fraction is
(a)$\frac{5}{6}$
(b)$\frac{6}{5}$
(c)$\frac{3}{8}$
(d)$\frac{8}{3}$
Answer
Answer (as printed): C
Explanation
Let the fraction be $\frac{x}{y}$. Then, $x+y=11$ $$\begin{aligned} & \frac{x+1}{y-2}=\frac{2}{3} \Rightarrow 3(x+1) \\ & =2(y-2) \Rightarrow 3 x-2 y=-7 \end{aligned}$$ Solving (i) and (ii), we get: $x=3$ and $y=8$. So, the fraction is $\frac{3}{8}$.
Explanation as extracted from the printed page; notation may be imperfect.