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 a very interesting question on the topic percentages using the concept of golden ratios. What is the golden ratio? Go go!! Google it.

Question 5 : A is x% more than B and is x% of sum of A and B. What is the value of x?

- 50%
- 62%
- 75%
- 37%

62%

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a = b (1 + x) => \\frac{a}{b}\\) = 1 + x

a = x (a + b), dividing by a through out

1 = x (1 + \\frac{b}{a}\\))

1 = x (1 + \\frac{1}{1/x}\\))

1 = x (\\frac{x+2}{x+1}\\))

x + 1 = x^{2} + 2x

=> x^{2} + x - 1 = 0

Now, we need to solve this equation. Using the discriminant method, when we solve this, x turns out to be \\frac{-1+√5}{2}\\).

x has to lie between 0 and 1 and there for cannot be \\frac{-1-√5}{2}\\)

So, the only solution is \\frac{-1+√5}{2}\\). This is roughly 0.62.

Or, x has to be 62% approximately. The ration 1.618 is also called the golden ratio, and is the conjugate and reciprocal of 0.618.

The golden ratio finds many mentions, from the Fibonacci series to Da Vinci. So, it is a big favourite of mathematician.

The question is **" What is the value of x? "**

x has to be 62% approximately.

Choice B is the correct answer.

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