# Difficult Percentages Solved QuestionAptitude Discussion

 Q. $B$ as a percentage of $A$ is equal to $A$ as a percentage of $(A + B)$. Find $B$ as a percentage of $A$.
 ✔ A. $62\%$ ✖ B. $73\%$ ✖ C. $41\%$ ✖ D. $57\%$

Solution:
Option(A) is correct

From the question stem, we know

$\dfrac{B}{A}=\dfrac{A}{A+B}$

As $B$ is a percent of $A$, let us assume $B=Ax$

Then, equation (1) can be re-written as

$x=\dfrac{1}{1+x}$

$\Rightarrow x(1+x)=1$

After this step, trial and error works best. The solution is $62\%$, answer choice ($A$) is the correct one.

Alternatively, solving, we get

$x^2+x+1=0$

$\Rightarrow x=\dfrac{-1+\sqrt{5}}{2}$

or

$\Rightarrow x=\dfrac{-1-\sqrt{5}}{2}$

So,

$\Rightarrow x=\dfrac{-1+\sqrt{5}}{2}$

$=0.62=62\%$

## (1) Comment(s)

Kotresh
()

If the percentage are different then how to solve such type of questions?