• # question_answer If the numerator of a fraction is increased by 200% and the denominator is increased by 160%, the resultant fraction is$\frac{7}{13}$. What is the original fraction? A)  $\frac{7}{15}$ B)         $\frac{2}{15}$ C)  $\frac{8}{15}$             D)  $\frac{5}{7}$

Solution :

Let the original fraction$=\frac{x}{y}$ According to the questions, $\frac{x+x\times 200%}{y+y\times 160%}=\frac{7}{13}$ $\Rightarrow$   $\frac{x+\frac{200x}{100}}{y+\frac{160y}{100}}=\frac{7}{13}=\frac{3x}{2.6y}=\frac{7}{13}$ $\Rightarrow$   $\frac{x}{y}=\frac{7}{13}\times \frac{26}{30}=\frac{7}{15}$ Hence, the original fraction is $\frac{7}{15}.$

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