Question

If the numerator of a fraction is increased by 200% and the denominator is increased by 300%, the resultant fraction is$\frac{5}{12}$. What was the original fraction?

• A. $\frac{12}{9}$
• B. $\frac{5}{9}$
• C. $\frac{11}{5}$
• D. $\frac{9}{5}$
• E. None of these

Answer 1

Answer: (B)

$\frac{5}{9}$

Answer 2

Let the original fraction be represented as $\frac{x}{y}$.

• Increasing the numerator by 200% means it becomes x + 2x = 3x
• Increasing the denominator by 300% means it becomes y + 3y = 4y
• The new fraction is$\frac{3x}{4y}$, and we know this equals $\frac{5}{12}$.
  So,$\frac{3x}{4y}$= $\frac{5}{12}$
  Now we need to find the original fraction x/y that satisfies this equation. Let's look at the options and see which one works.
• Option (1):$\frac{12}{9}$
• If we increase the numerator by 200%, we get 3*12 = 36
• If we increase the denominator by 300%, we get 4*9 = 36
• The new fraction would be$\frac{36}{36}$= 1, which is not$\frac{5}{12}$. So this is incorrect.
• Option (2): $\frac{5}{9}$
• Increased numerator: 3*5 = 15
• Increased denominator: 4*9 = 36
• New fraction:$\frac{15}{36}$=$\frac{5}{12}$. This matches the given information!
  Therefore, the original fraction was$\frac{5}{9}$.
  Final Answer: (2) $\frac{5}{9}$
  The Correct option is(B)