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

The Correct Option is B

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)