Reverse-engineering an original fraction: After increasing the numerator of a fraction by 200% and the denominator by 150%, the resulting fraction is 9/35. What was the original fraction?

Introduction / Context:Percentage increases on the numerator and denominator scale a fraction multiplicatively. “Increased by 200%” means the new numerator equals old numerator × 3. “Increased by 150%” means the new denominator equals old denominator × 2.5. You are given the final fraction and must recover the original one by reversing these multiplicative effects.

Given Data / Assumptions:

• Let the original fraction be n/d.
• New numerator after +200%: 3n.
• New denominator after +150%: 2.5d.
• Resulting fraction = 9/35.

Concept / Approach:Set 3n / (2.5d) = 9/35. Solve for the ratio n/d by isolating it on one side. The operations are pure scaling; there is no need to assume integer numerators or denominators at intermediate steps. Finally, simplify the result to lowest terms to match one of the options.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 3/10, 2/15, 2/7: After applying the same percentage increases, these do not yield 9/35; numerical checks disagree.

Common Pitfalls:

• Misreading “increased by 200%” as “becomes 200%” (×2) instead of ×3.
• Forgetting that +150% equals ×2.5, not ×1.5 of the denominator.

Final Answer: