The golden ratio is a wonderful concept. Go on, google it.
$a = b (1 + x)$
$\Rightarrow a/b = 1 + x$
$\Rightarrow a = x (a + b),$ dividing by a through out
$\Rightarrow 1 = x (1 + b/a)$
$\Rightarrow 1 = x \left(1 + \dfrac{1}{\frac {1}{x}}\right)$
$\Rightarrow 1 = x\left(\dfrac{x+2}{x+1}\right)$
$ \Rightarrow x + 1 = x^2 + 2x$
$\Rightarrow x^2 + x - 1 = 0$
Now, we need to solve this equation. Using the discriminant method, when we solve this, $x$ turns out to be $\dfrac{−1+√5}{2}.$
$x$ has to lie between $0$ and $1$ and there for cannot be $\dfrac{−1−√5}{2}$
So, the only solution is $\dfrac{−1+√5}{2}$. 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.
Hence, the answer is 62%
Choice B is the correct answer.
