 # If the numerator of a fraction is increased by 200% and the denominator is increased by 350%, the resultant fraction is $\dfrac{5}{12}$. What is the original fraction?(a) $\dfrac{5}{9}$(b) $\dfrac{5}{8}$(c) $\dfrac{7}{12}$(d) $\dfrac{11}{12}$(e) None of these
Hint: To solve the problem, we start by assuming a fraction with numerator as x and the denominator as y. We then use the given conditions and then equate it to $\dfrac{5}{12}$. We can then find the value of x and y.
We start the problem by assuming the fraction as $\dfrac{x}{y}$. That is we assume the numerator as x and the denominator as y. Now, we are given that the numerator is increased by 200% and the denominator is increased by 350%. Thus, we have that the new numerator is 3x (since, 200% of x is 2x and thus increasing x by 2x, we get x + 2x = 3x). Similarly, for the denominator, we have the new denominator as 4.5y (since, 350% of y is 3.5y and thus increasing y by 3.5y, we get y + 3.5y = 4.5y). Equating this to $\dfrac{5}{12}$, we have,
\begin{align} & \Rightarrow \dfrac{3x}{4.5y}=\dfrac{5}{12} \\ & \Rightarrow \dfrac{x}{y}=\dfrac{5}{12}\times \dfrac{4.5}{3} \\ & \Rightarrow \dfrac{x}{y}=\dfrac{22.5}{36}=\dfrac{7.5}{12}=\dfrac{5}{8} \\ \end{align}
Hence, the correct answer is (b) $\dfrac{5}{8}$.
Note: While solving the problem, $\dfrac{3x}{4.5y}=\dfrac{5}{12}$ (where, x is the numerator of the original number, y is the denominator of the original number), we see that there are 2 variables for 1 equation. Thus, the problem is explicitly not solvable. However, we are still able to find the required answer since we only have to find the ratio (that is $\dfrac{x}{y}$) and thus we only require this one equation to get the value of original fraction.