What constant must be added to both numerator and denominator of 3/4 so that the resulting fraction equals 11/12?

Introduction / Context:Adjusting a fraction by adding the same constant to its numerator and denominator changes its value in a predictable way. The task is to find the constant that transforms 3/4 into 11/12. Cross-multiplication is the cleanest route to a solution.

Given Data / Assumptions:

• We need k such that (3 + k) / (4 + k) = 11/12.
• k is a real number; in typical aptitude settings an integer solution is expected.

Concept / Approach:Set up the proportion and cross-multiply to produce a linear equation in k. Solve for k and verify by substitution back into the fraction. This avoids any guesswork and works for any target ratio.

Step-by-Step Solution:

Verification / Alternative check:Substitute back: (3 + 8)/(4 + 8) = 11/12; numerically 11/12 equals 11/12. Verified.

Why Other Options Are Wrong:5, 6, 7, and 9 yield (3 + k)/(4 + k) values different from 11/12 upon substitution.

Common Pitfalls:Adding to only the numerator or only the denominator; arithmetic slips when cross-multiplying; or canceling terms prematurely.

Final Answer:8