Test your understanding of percentages, percentage increase and decrease, and algebraic constraints with this CAT-level Future Year Question from GRADSKOOL.
This question combines percentage change with integer conditions and requires careful interpretation of both relative and absolute changes.
Two positive integers X and Y satisfy X + Y = 1000, with X a multiple of 25. X is increased by 20%, and Y is decreased by L% (where L is a positive multiple of 5, L ≤ 60), resulting in a combined total that is exactly 8% more than the original 1000.
Given that the actual amount by which Y decreases (in absolute terms) is exactly 60, find X.
A. 600
B. 800
C. 850
D. 700
Before watching the solution, try to solve the question using the information about the original total, the percentage increase in X, and the absolute decrease in Y.
Pay particular attention to the distinction between a percentage decrease and the actual amount of decrease.
The primary concept tested is Percentages, specifically percentage increase and percentage decrease.
The question also involves:
This question belongs to:
Quantitative Aptitude → Arithmetic → Percentages
Start by determining the new combined total after the overall 8% increase.
Then use the fact that the actual decrease in Y is given directly as 60.
Represent the 20% increase in X algebraically and combine it with the original relationship X + Y = 1000.
The key is to use the absolute decrease of 60 directly rather than unnecessarily solving for L first.
Once you obtain a candidate value for X, verify it against all the conditions given in the question.
CAT questions involving percentages often include more information than is necessary for the most efficient solution.
A useful skill is identifying whether a percentage is being given as:
In this question, the absolute decrease in Y is explicitly provided. Recognizing this can significantly simplify the setup.
Difficulty: Moderate
The calculations involved are not particularly complex, but the question contains multiple constraints that must be interpreted correctly. The main challenge is identifying the most useful information and setting up the percentage changes without unnecessary casework.
Have you solved it?
Watch the complete video solution for the step-by-step approach and final answer.
https://www.youtube.com/watch?v=LMEo5wsJobM
The primary concept tested is Percentages, with emphasis on percentage increase, percentage decrease and absolute change.
This question belongs to CAT Quantitative Aptitude, specifically the Arithmetic → Percentages area.
The key idea is to distinguish between the percentage decrease in Y and the actual amount by which Y decreases. The question directly provides the absolute decrease as 60.
This is a Moderate difficulty CAT-level Future Year Question because it combines percentage calculations with multiple algebraic and integer constraints.
Yes. Attempt the question independently first, then watch the complete video solution to compare your approach and reasoning.