If a divided by (a + b) equals 15 divided by 21, that is a / (a + b) = 15 / 21, what is the value of the ratio (a + b) / (a - b)?

Introduction / Context:

This ratio and proportion question is typical of aptitude exams. You are given a relationship between a and (a + b) and asked to transform it to get another ratio involving (a + b) and (a - b). The task is to use algebraic manipulation, not guesswork.

Given Data / Assumptions:

• a / (a + b) = 15 / 21.
• a and b are real numbers with a + b not equal to zero.
• We need to find (a + b) / (a - b).

Concept / Approach:

First simplify the fraction 15 / 21, then cross multiply to get a relation between a and b. Once the simple ratio between a and b is obtained, substitute convenient values that satisfy that ratio and then compute (a + b) / (a - b). Using simple multiples keeps calculations easy and avoids unnecessary complexity.

Step-by-Step Solution:

Verification / Alternative check:

Take k = 1. Then a = 5 and b = 2. Check the original ratio: a / (a + b) = 5 / 7, which matches the simplified version of 15 / 21. Then (a + b) / (a - b) = 7 / 3, which confirms the result.

Why Other Options Are Wrong:

The values 13/9, 23/11, 14/5, and 21/9 do not match the derived ratio for any consistent a and b that satisfy a / (a + b) = 15 / 21. They correspond to incorrect algebraic manipulations or incomplete simplification.

Common Pitfalls:

Errors often occur when cross multiplying or when simplifying 15 / 21. Another common mistake is to misinterpret the given ratio as a : b rather than a : (a + b), which leads to a completely different relation.

Final Answer:

The value of (a + b) / (a - b) is 7/3.