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? [SBI Jr. Associates (Pre.) Exam, 2016]
(a)$\frac{22}{5}$
(b)$\frac{24}{5}$
(c)$\frac{27}{6}$
(d)$\frac{28}{5}$
(e)$\frac{30}{11}$
Answer
Answer (as printed): D
Explanation
Let original fraction be $\frac{a}{b}$. Now, according to the question $$\begin{aligned} & \frac{a-a \times \frac{25}{100}}{b+b \times \frac{250}{100}}=\frac{6}{5} \\ & \frac{0.75 a}{3.50 b}=\frac{6}{5} \\ & \Rightarrow \frac{a}{b}=\frac{6}{5} \times \frac{3.50}{0.75}=\frac{6 \times 350 \times 100}{5 \times 75 \times 100}=\frac{28}{5} \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.