If the numerator of a fraction is increased b | vedclass

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Question

(A) Let the original fraction be $\frac{x}{y}$.According to the problem,the numerator is increased by $150 \%$,so the new numerator becomes $x + 1.5x

Vedclass · Accepted Answer

$\frac{4}{9}$

Vedclass · Answer

(A) Let the original fraction be $\frac{x}{y}$.According to the problem,the numerator is increased by $150 \%$,so the new numerator becomes $x + 1.5x = 2.5x$.The denominator is increased by $300 \%$,so the new denominator becomes $y + 3y = 4y$.The resulting fraction is given as $\frac{2.5x}{4y} = \frac{5}{18}$.To simplify,multiply the numerator and denominator by $10$ to remove the decimal: $\frac{25x}{40y} = \frac{5}{18}$.Simplifying the fraction $\frac{25}{40}$ gives $\frac{5}{8}$,so $\frac{5x}{8y} = \frac{5}{18}$.Multiplying both sides by $\frac{8}{5}$,we get $\frac{x}{y} = \frac{5}{18} 	imes \frac{8}{5} = \frac{8}{18} = \frac{4}{9}$.Thus,the original fraction is $\frac{4}{9}$.

If the numerator of a fraction is increased by $150 \%$ and the denominator of the fraction is increased by $300 \%$,the resultant fraction is $\frac{5}{18}$. What is the original fraction?

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