# CAT Quantitative Aptitude Questions | CAT Percentages Problems - Integers

###### CAT Questions | Percentage Questions | Percentage - Integers

The question is from CAT Percentages. 2IIMs CAT question bank provides you with CAT questions that can help you gear for CAT Exam CAT 2023. This question is from the topic percentages using the concept of golden ratios. The golden ratio idea is so interesting that we have repeated it.

Question 11 : a is x % of b, b is x% more than a. Find x.

1. 50%
2. 62%
3. 75%
4. 37%

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##### Method of solving this CAT Question from Percentages: The golden ratio idea is so interesting that we have repeated it.

a = bx
b = a (1 + x), substituting this in the previous equation, we get
x (x + 1) = 1
x2 + x - 1 = 0 or
x is approximately 0.62 or 62%. The ration 1.618 is also called the golden ratio, and is the conjugate and reciprocal of 0.618.

##### Hence, the answer is 62%

Choice B is the correct answer.

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