The numerator of a fraction is decreased by 25% and the denominator is increased by 250%. If the resultant fraction is $$\frac{6}{5}$$, what is the original fraction ?

A. $$\frac{22}{5}$$

B. $$\frac{24}{5}$$

C. $$\frac{27}{6}$$

D. $$\frac{28}{5}$$

E. $$\frac{30}{11}$$

Answer: Option D

Solution(By Examveda Team)

Let original fraction be $$\frac{a}{b}$$
Now, according to the question,
$$\eqalign{ & \Leftrightarrow \frac{{a - a \times \frac{{25}}{{100}}}}{{b + b \times \frac{{250}}{{100}}}} = \frac{6}{5} \cr & \Rightarrow \frac{{0.75a}}{{3.50b}} = \frac{6}{5} \cr & \Rightarrow \frac{a}{b} = \frac{6}{5} \times \frac{{3.50}}{{0.75}} \cr & \Rightarrow \frac{a}{b} = \frac{{6 \times 350 \times 100}}{{5 \times 75 \times 100}} \cr & \Rightarrow \frac{a}{b} = \frac{{28}}{5} \cr} $$