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1. A fraction is such that if the double of the numerator and the triple pf the denominator is changed by +10 percent and -30 percent respectively, then we get 11 percent of $\frac{16}{21}$ . Find the fraction :

A. $\frac{2}{25}$

B. $\frac{3}{25}$

C. $\frac{4}{25}$

D. None of these

Solution:

Let the fraction be

\frac{x}{y}

Then,

\begin{aligned} \Leftrightarrow \frac{110 % of 2 x}{70 % of 3 y} = 11 % of \frac{16}{21} \\ \Leftrightarrow \frac{22 x}{21 y} = \frac{11}{100} \times \frac{16}{21} \\ \Leftrightarrow \frac{x}{y} = (\frac{11}{100} \times \frac{16}{21} \times \frac{21}{22}) \\ \Leftrightarrow \frac{x}{y} = \frac{2}{25} \end{aligned}

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