# CAT Quantitative Aptitude Questions | CAT Percentages Problems - Variables

###### CAT Questions | Percentage Questions | Percentages - Algebra & Inequalities
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The question is from CAT Percentages. CAT tests multiple ideas in the same question, and 2IIMs CAT question bank provides you with CAT questions that can help you gear for CAT Exam CAT 2020. This question from the topic percentages using variables.When Percentages, Algebra and Inequalities are combined it proves to be a Potent cocktail.Go get a taste of it.

Question 14 : A is x % more than B. B is y % less than C. If A, B and C are positive and A is greater than C, find the relation between x and y.

1. y (100 - x) < 100x
2. y (100 - x) > 100x
3. y (100 + x) < 100x
4. y (100 + x) > 100x

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##### Method of solving this CAT Question from Percentages: Again comparison of A, B and C but in terms of x and y.

a = (1 + x) b
b = c (1 - y)
c = $$frac{b}{1 - y}\\$ a is greater than c or b$1 + x) > $$frac{b}{1 - y}\\$ => 1 + x > $\frac{1}{1 - y}\\$ =>$1 + x) (1 - y) > 1
=> 1 + x - y - xy > 1
=> x > y (1 + x)
Converting back to percentages...

=> $$frac{x}{100}\\$ > $\frac{y}{100}\\$$$$frac{100}{100}\\$ + $\frac{x}{100}\\$) Therefore, y$100 + x) < 100x

The question is " find the relation between x and y. "

##### Hence, the answer is y (100 + x) < 100x

Choice C is the correct answer.

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