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1. 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 he 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. $\frac{17}{21}$

Solution:

Let the fraction be

\frac{x}{y}

Then,

\begin{aligned} \Leftrightarrow \frac{x + 2}{y + 3} = \frac{7}{9} \\ \Leftrightarrow 9 x - 7 y = 3..... (i) \\ And, \\ \Leftrightarrow \frac{x - 1}{y - 1} = \frac{4}{5} \\ \Leftrightarrow 5 x - 4 y = 1..... (i i) \end{aligned}

Solving (i) and (ii), we get :
x = 5 and y = 6
Hence, the original fraction is

\frac{5}{6}

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