CAT Quantitative Aptitude Questions | CAT Percentages Problems - Variables

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The question is from CAT Percentages. 2IIMs CAT question bank provides you with CAT questions that can help you gear for CAT Exam CAT 2019. This is a very interesting question from the topic percentages using variables.When x's and y's get thrown about, questions always seem harder. But knowing how to deal with these is very crucial.

Question 7 : A is x% less than B, A is y% less than C. C is k% more than B. Express k in terms of x and y.

  1. \\frac{(y - x)100}{100 - y}\\)
  2. \\frac{(y + x)100}{100 - y}\\)
  3. \\frac{(y - x)100}{100 - x}\\)
  4. \\frac{(y - x)100}{100 + y}\\)

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Explanatory Answer

Method of solving this CAT Question from Percentages: Comparison of A, B and C in terms of x and k.

A = B(1 - \\frac{x}{100}\\)) -------- Equation (1)
A = C(1 - \\frac{y}{100}\\)) ------Equation (2)
C = B(1 + \\frac{k}{100}\\)) -------- Equation (3)
Substituting equations (1) and (3) in (2), we get
B(1 + \\frac{k}{100}\\)) (1 - \\frac{y}{100}\\)) = B(1 - \\frac{x}{100}\\))
1 + \\frac{k}{100}\\) - \\frac{y}{100}\\) - \\frac{ky}{100^2}\\) = 1 - \\frac{x}{100}\\)
\\frac{k}{100}\\) (1 - \\frac{y}{100}\\)) = \\frac{y - x}{100}\\)
k = (\\frac{(y - x)100}{100 - y}\\))

The question is " Express k in terms of x and y. "

Hence, the answer is k = (\\frac{(y - x)100}{100 - y}\\))

Choice A is the correct answer.


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