The income of A is 25% more than the income of B.\nB's income is what percentage of A's income?

Introduction / Context:
This problem checks understanding of percentage increase and how to reverse it to express one quantity as a percentage of another. Many exam questions use relationships between salaries, prices, or marks in exactly this way, so it is important to convert sentences about "more than" or "less than" into simple algebraic expressions.

Given Data / Assumptions:

• Income of A is 25% more than income of B.
• We need B's income expressed as a percentage of A's income.
• No actual rupee values are given, so we can assume a convenient value for B.

Concept / Approach:
When one quantity is a certain percent more than another, we express the larger as a multiple of the smaller. If A is 25% more than B, then A = B * (1 + 25/100) = 1.25 * B. To find B as a percentage of A, we compute B / A and convert that ratio to a percent. Using algebra with assumed values keeps the calculation simple and free from confusion.

Step-by-Step Solution:
Step 1: Let the income of B be 100 units (this is a convenient assumption).Step 2: Then the income of A is 25% more than 100 units.Step 3: A = 100 * (1 + 25/100) = 100 * 1.25 = 125 units.Step 4: Now compute B as a fraction of A: B / A = 100 / 125.Step 5: Convert this ratio into a percentage: (100 / 125) * 100% = 80%.

Verification / Alternative check:
Instead of assuming B = 100, we can use algebra. Let B = b. Then A = 1.25 * b. The required percentage is (b / (1.25 * b)) * 100 = (1 / 1.25) * 100. Since 1 / 1.25 = 0.8, the result is 0.8 * 100 = 80%. Both approaches agree, so the result is verified.

Why Other Options Are Wrong:
75% would be correct if A was 33.33% more than B, not 25% more, so it does not match the condition here.
50% would mean B has half the income of A, which contradicts A being only 25% higher than B.
25% would suggest B is much smaller compared to A, which is not consistent with the given relation.
60% also does not come from the ratio of 100 to 125 and is simply another distractor value.

Common Pitfalls:
Candidates often confuse "A is 25% more than B" with "A is 125% of B" and then misinterpret which quantity should be in the numerator when forming the fraction. Another common error is trying to subtract 25 from 100 directly without forming the correct ratio. Always remember that when converting one quantity to a percentage of another, you divide the first by the second and then multiply by 100, keeping the correct order of numerator and denominator.

Final Answer:
B's income is 80% of A's income.