The sum of the numerator and denominator of a fraction is 11. If 1 is added to the numerator and 2 is subtracted from the denominator, it becomes $$\frac{2}{3}$$. The fraction is :
Options:
A . $$\frac{5}{6}$$
B . $$\frac{6}{5}$$
C . $$\frac{3}{8}$$
D . $$\frac{8}{3}$$
Answer: Option C Let the fraction be $$\frac{x}{y}$$ Then, $$\eqalign{ & \Leftrightarrow x + y = 11.....(\text{i}) \cr & \Leftrightarrow \frac{{x + 1}}{{y - 2}} = \frac{2}{3} \cr & \Leftrightarrow 3\left( {x + 1} \right) = 2\left( {y - 2} \right) \cr & \Leftrightarrow 3x - 2y = - 7.....(\text{ii}) \cr} $$ Solving (i) and (ii), we get: x = 3 and y = 8 So, the fraction is $$\frac{3}{8}$$
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