If the numerator of a fraction is increased by 15% and its denominator is decreased by 8%,
the new fraction becomes 15/16. Find the original fraction.
A. 4/3
B. 15/4
C. 3/4
D. 4/15

Solving the Original Fraction Problem

This is a classic math problem involving percentage change in both the numerator and denominator of a fraction. Let’s break it down step by step.

📌 Problem Statement

If the numerator of a fraction is increased by 15% and the denominator is decreased by 8%, the new fraction becomes 15/16. Find the original fraction.

Step-by-Step Solution

Let the original fraction be:

Original = x / y

Apply the percentage changes:

• Numerator becomes: x + 15% of x = x(1 + 15/100) = 1.15x
• Denominator becomes: y - 8% of y = y(1 - 8/100) = 0.92y

Now, the new fraction becomes:

(1.15x) / (0.92y) = 15 / 16

Cross-multiply:

1.15x × 16 = 15 × 0.92y
18.4x = 13.8y

Solve for x/y:

x / y = 13.8 / 18.4 = 69 / 92 = 3 / 4

✅ Final Answer: C. 3/4

Key Takeaways:

• Convert percentage increases and decreases into decimal multipliers.
• Use algebra and cross-multiplication to solve the resulting equation.
• Simplify fractions to get the most accurate and understandable result.