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1. If the numerator of a fraction is increased by 200% and the denominator is increased by 300%, the resultant fraction is $\frac{15}{26}$ . What was the original fraction ?

A. $\frac{8}{11}$

B. $\frac{10}{11}$

C. $\frac{9}{13}$

D. $\frac{10}{13}$

Solution:

Let the fraction be

\frac{x}{y}

Then,

\begin{aligned} \Leftrightarrow \frac{x + 200 % of x}{y + 300 % of y} = \frac{15}{26} \\ \Leftrightarrow \frac{3 x}{4 y} = \frac{15}{26} \\ \Leftrightarrow \frac{x}{y} = \frac{15}{26} \times \frac{4}{3} \\ \Leftrightarrow \frac{x}{y} = \frac{10}{13} \end{aligned}

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