Correct option is (C) 5/7
Let fraction be \(\frac xy.\)
According to given conditions, we have
\(\frac{x+9}y=2\) and
\(\frac{x}{y-2}=1\)
\(\Rightarrow\) x+9 = 2y and x = y - 2
\(\Rightarrow\) x - 2y + 9 = 0 __________(1)
and x - y + 2 = 0 __________(2)
Put x = y - 2 from (2) into (1), we get
y - 2 - 2y + 9 = 0
\(\Rightarrow\) 2y - y = 9 - 2
\(\Rightarrow\) y = 7
\(\therefore\) x = y - 2
= 7 - 2 = 5 (From (2))
Hence, the fraction is \(\frac xy=\frac{5}{7}.\)
