If A’s income is 5/6 of B’s income, by what percent is B’s income more than A’s income?

Introduction / Context:Problems comparing two quantities often ask “how much percent more/less.” The base for the percentage must be the quantity named after “than”. Here, B is compared to A, so A is the base.

Given Data / Assumptions:

• A = (5/6) * B.
• Find ((B − A)/A) * 100.

Concept / Approach:From A = (5/6)B, divide both sides by A to express B in terms of A, or directly compute (B − A)/A. This yields the percentage by which B exceeds A.

Step-by-Step Solution:A = (5/6)B ⇒ B − A = B − (5/6)B = (1/6)B(B − A)/A = [(1/6)B] / [(5/6)B] = 1/5Percentage = (1/5) * 100 = 20%

Verification / Alternative check:Let B = 60. Then A = 50. B is 10 more than A; 10/50 = 20%—consistent.

Why Other Options Are Wrong:12 1/2%, 15%, 16 2/3%, 25% stem from choosing the wrong base or arithmetic slips.

Common Pitfalls:Using B as the base (computing (B − A)/B), which answers a different question and gives 16 2/3% instead of the requested 20%.

Final Answer:20%