Subject: General Aptitude · Chapter: Problems on Numbers · Exam: · Marks: · Difficulty:
A fraction becomes $\frac{2}{3}$ when 1 is added to both its numerator and denominator. And, it becomes $\frac{1}{2}$ when 1 is subtracted from both the numerator and denominator. Find the fraction.
Answer
SELF-PRACTICE — the source book printed no answer.
Nothing is invented here, so this question has no answer on record.
Explanation
Let the required fraction be $\frac{x}{y}$. Then, $$\frac{x+1}{y+1}=\frac{2}{3} \Rightarrow 3 x-2 y=-1 \ldots(i) \text { and } \frac{x-1}{y-1}=\frac{1}{2} \Rightarrow 2 x-y=1$$ Solving (i) and (ii), we get : $x=3, y=5$. $$\text { ∴ } \text { Required fraction }=\frac{3}{5} .$$
Explanation as extracted from the printed page; notation may be imperfect.