Question

If the numerator of a certain fraction is increased by 2 and the denominator increased by 1, then the resulting fraction equals \(\frac{1}{2}\) If however the numerator is increased by 1 and the denominator decreased by 2, then the resulting fraction equal \(\frac{3}{5}\) Find the fraction.

Answer 1

Let the given fraction be \(\frac{X}{y}\).Then,

\(\frac{X+2}{y+1}\)= \(\frac{1}{2}\) \(\Rightarrow\) 2x + 4 =y + 1  \(\Rightarrow\) 2x – y = – 3 ..........(i)

\(\frac{X+1}{y-2}\) = \(\frac{3}{5}\) \(\Rightarrow\) 5x + 5 = 3y - 6  \(\Rightarrow\) 5x – 3y = –11 ..........(ii)

Now,

Putting x = 2 in equation (1), we get

4 – y = – 3  \(\Rightarrow\) – y = – 3 – 4 \(\Rightarrow\) y = 7

\(\therefore\) The given fraction is \(\frac{2}{7}\)