Subject: General Aptitude · Chapter: Problems on Numbers · Exam: · Marks: · Difficulty:
If the numerator of a fraction is increased by 2 and the denominator is increased by 3, the fraction becomes $\frac{7}{9}$ and if both the numerator as well as the denominator are decreased by 1 , the fraction becomes $\frac{4}{5}$. What is the original fraction?
(a)$\frac{5}{6}$
(b)$\frac{9}{11}$
(c)$\frac{13}{16}$
(d)$\frac{17}{21}$
Answer
Answer (as printed): A
Explanation
Let the fraction be $\frac{x}{y}$. Then, $$\frac{x+2}{y+3}=\frac{7}{9} \Leftrightarrow 9 x-7 y=3$$ and $$\frac{x-1}{y-1}=\frac{4}{5} \Leftrightarrow 5 x-4 y=1$$ Solving (i) and (ii), we get : $x=5, y=6$. Hence, the original fraction is $\frac{5}{6}$.
Explanation as extracted from the printed page; notation may be imperfect.