Question

A fraction in reduced form is such that when it is squared and then its numerator is increased by $25\%$ and the denominator is reduced to $80\%$ it results in $5/8$ of the original fraction. The product of the numerator and denominator is.

• A. $6$
• B. $12$
• C. $10$
• D. $7$

Answer 1

Answer: (C)

$10$

Let the fraction be $\frac{100x}{100y}$

Now according to the question,

$\frac{125x^2}{80y^2}=\frac{25x^2}{16y^2}=\frac{5}{8}\times \frac{100x}{100y}$

$\frac{25x^2}{16y^2}=\frac{5}{8}\times \frac{100x}{100y}$

$\therefore \frac{100x}{100y}=\frac{5}{2}$.

Hence, product of numerator and denominator = $2\times 5=10$.