X’s income is 20% more than that of Y. What percent is Y’s income less than X?

Appeared in: RRB Staff Nurse Mumbai-2015

Explanation

The core of this problem is understanding that the base for comparison changes.
First, establish X's income relative to Y. If Y is 100, X is 120 (20% more).
The difference in their incomes is 20.
To find how much less Y's income is than X's, the difference (20) must be divided by X's income (120), not Y's.
The calculation is (20 / 120) * 100, which simplifies to (1/6) * 100.
This results in 16.66...%, which is expressed as the fraction 16⅔%.

Option A: This is an incorrect calculation. It does not correspond to the correct fraction (1/6) derived from the problem.
Option C: This is a common error. It incorrectly assumes the percentage decrease is the same as the percentage increase. While Y's income is ₹20 less than X's, ₹20 is not 20% of ₹120.
Option D: This is an incorrect calculation. It likely results from a miscalculation of the fraction or the final percentage.

Visual 1: Infographic: A bar chart comparing two bars, one labeled 'Y's Income (100)' and a taller one labeled 'X's Income (120)'. An arrow from the top of Y to the top of X shows '+20%', and another arrow from the top of X down to the top of Y shows '-16⅔%' to visually demonstrate the change in the base of the percentage.

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.
This type of question is not directly related to clinical nursing practice but tests general aptitude and numerical reasoning, which are components of many nursing entrance and competitive examinations.
What if? - If the stem changed one defining clue so that 16⅔% no longer matched, reassess the option whose mechanism, classification, or indication now fits the revised presentation.

How to Approach the Question

First, identify the initial value and the percentage increase. Let the initial value (Y's income) be 100 for simplicity.
Calculate the new value (X's income) by adding the percentage increase: 100 + (20% of 100) = 120.
Determine the absolute difference between the new and original values: 120 - 100 = 20.
Identify the base for the second part of the question. It asks 'less than X', so X's income (120) is the new base.
Calculate the percentage decrease using the new base: (Difference / New Base) * 100 = (20 / 120) * 100.
Simplify the fraction (20/120 = 1/6) and convert to a percentage to find the final answer.

Concept Tested & Keywords

QLgrV54Vmn0Y0e1_sxQls5

Practise the full RRB Staff Nurse Mumbai-2015

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