This CAT-level Future Year Question tests the concept of successive percentage increases through a comparison of the incomes of A, B, and C.
The question requires careful interpretation of percentage relationships between successive quantities rather than simply adding the two percentage increases.
A’s income is R% more than B’s, and B’s income is R% more than C’s, where R is a positive integer. If A’s income exceeds C’s by exactly 69%, find R.
Before watching the solution, express the income of B as a percentage of C and then express A’s income in terms of B.
Remember that two successive increases of R% do not result in a simple 2R% increase.
The primary concept tested is Successive Percentage Change.
The question specifically tests:
- Successive percentage increases
- Percentage comparison between quantities
- Multiplicative effect of percentage changes
- Forming and solving a percentage equation
Quantitative Aptitude → Arithmetic → Percentages
Take C’s income as a convenient base value.
Since B is R% more than C, express B in terms of C.
Then use the fact that A is R% more than B to express A in terms of C.
Finally, compare A directly with C using the given 69% increase.
The important idea is that the two R% increases are successive, so their effects multiply rather than simply add.
When the same percentage increase occurs successively, avoid treating it as a single increase of twice the percentage.
For example, two successive increases of R% result in a total multiplier of:
(1 + R/100)²
This is different from simply using:
1 + 2R/100
Recognizing this distinction is fundamental to solving CAT percentage questions efficiently.
1. Assuming that two successive R% increases result in a 2R% increase.
2. Taking A’s income as R% more than C’s directly.
3. Forgetting that the second percentage increase is applied to the already increased income of B.
4. Using the wrong base while calculating the percentage increase.
Difficulty: Easy
The question tests a standard successive-percentage concept with a single unknown and a clean numerical condition. The primary challenge is setting up the successive increases correctly.
Try solving the question first.
Then watch the complete video solution for the detailed approach and final answer:
https://www.youtube.com/watch?v=ZfJEcklNCBA
- Successive Percentage Change
- Percentage Increase and Decrease
- Percentage Comparison
- Ratio and Percentage
- CAT Arithmetic
- CAT Quantitative Aptitude
Q. What concept is tested in this CAT Future Year Question?
The primary concept tested is successive percentage increase.
Q. Which CAT section does this question belong to?
It belongs to CAT Quantitative Aptitude → Arithmetic → Percentages.
Q. Why can’t successive percentage increases simply be added?
Because each successive percentage increase is calculated on the newly increased value, not the original value.
Q. What is the key formula for two successive increases of R%?
The resulting multiplier is:
(1 + R/100)²
The total percentage increase is therefore not simply 2R%.
Q. What is the difficulty level of this FYQ?
This is an Easy CAT-level Future Year Question focused on the fundamental concept of successive percentage change.