If increasing the numerator by 20% and decreasing the denominator by 10% yields a value of 16/21, what is the original fraction?

Introduction / Context:
Transformations of fractions via percentage changes are best handled algebraically. Treat the original fraction as x/y, apply the specified changes to numerator and denominator, and equate to the given resultant value.

Given Data / Assumptions:

• Original fraction = x/y with y ≠ 0.
• New fraction = (1.20x) / (0.90y) = 16/21.
• All changes are exact percentages.

Concept / Approach:
Simplify the multiplier (1.20/0.90) to 4/3. Then (4/3)*(x/y) = 16/21 ⇒ x/y = (16/21) * (3/4). Reduce to lowest terms for clarity.

Step-by-Step Solution:

Verification / Alternative check:
Start from 4/7: Increase numerator by 20% ⇒ 4.8; decrease denominator by 10% ⇒ 6.3; new value = 4.8/6.3 = 48/63 = 16/21. Yes.

Why Other Options Are Wrong:
3/5 and 2/3 are common guesses from adding or subtracting percentages; 5/7 is close but incorrect after the transformation.

Common Pitfalls:
Adding 20% and 10% or treating them as changes on the entire fraction rather than separate numerator and denominator adjustments.

Final Answer:
4/7