X's income is 20% more than Y's income. Y's income is less than X's income by

Appeared in: RRB Staff Nurse Ahmedabad-2015

Explanation

To solve this, assume a base income for Y, such as ₹100. Since X's income is 20% more, X's income becomes ₹120.
The question asks for the percentage by which Y's income is less than X's. This means X's income (₹120) is the base for the calculation.
The difference in income is ₹20. The percentage is calculated as (Difference / Base) × 100, which is (20 / 120) × 100.
Simplifying the fraction (20/120) gives 1/6. Multiplying by 100 gives 16.66..., which is equivalent to 16 2/3%.

Option A: This is an incorrect calculation. It does not correspond to the correct formula for percentage decrease from a larger base.
Option C: This is a common mistake. It incorrectly assumes that the percentage increase and decrease between two numbers are symmetrical. The percentage difference depends on the base value used for comparison.
Option D: This is an incorrect calculation. It does not result from the correct application of the percentage change formula.

Visual 1: Infographic - A bar chart comparing X's income (120 units) and Y's income (100 units). Arrows can illustrate the +20% increase from Y to X and the -16 2/3% decrease from X to Y, highlighting the different base values used in each calculation.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Percentage Change and Comparison as background academic context rather than a clinical decision trigger.
While this is a mathematics question, the skill of interpreting percentage changes is crucial in nursing for tasks like calculating drug dosage adjustments, understanding changes in lab values, or analyzing patient weight fluctuations.
What if? If the question asked 'X's income is 20% less than Y's income, by what percentage is Y's income more than X's?', the base would change. Let Y=100, then X=80. The difference is 20. The new calculation would be (20/80) × 100 = 25%.

How to Approach the Question

Step 1: Identify the core comparison in the question: 'Y's income is less than X's income by...'. This tells you the base for your percentage calculation is X's income.
Step 2: To simplify the calculation, assume a starting value for the initial quantity. Let Y's income be 100.
Step 3: Calculate the other value based on the information given. X's income is 20% more than Y's, so X = 100 + (20% of 100) = 120.
Step 4: Find the absolute difference between the two values: 120 - 100 = 20.
Step 5: Apply the percentage change formula: (Difference / Base Value) × 100. In this case, it is (20 / 120) × 100.
Step 6: Simplify the fraction (20/120 = 1/6) and calculate the final percentage: (1/6) × 100 = 16.66...%, which is 16 2/3%.

Concept Tested & Keywords

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Attempt every question from this paper in a timed mock, then review the full solution for each one.