Question

If A is 150% of B then B is what percent of A + B?

Answer 1

Hint: First of all, write A in terms of B by using the relation that A is 150% of B as $A=\dfrac{150}{100}B$ then simplification of this relation between A and B can give $A=\dfrac{3}{2}B$. Write A + B which in terms of B because we have to find B is what percent of A + B then divide B by A + B and then multiply by 100 to get the answer in percentage.

Complete step-by-step solution -
It is given that A is 150% of B so writing A in terms of B we get,
$A=\dfrac{150}{100}B$
Simplifying the above relation we get,
$A=\dfrac{3}{2}B$
Writing A + B in terms of B we get,
$\begin{align}
  & A+B=\dfrac{3}{2}B+B \\
 & \Rightarrow A+B=\dfrac{5}{2}B \\
\end{align}$
We have asked to find B is what percent of A + B so we are going to divide B by A + B then multiply this division by 100.
$\begin{align}
  & \dfrac{B}{A+B}\times 100 \\
 & =\dfrac{B}{\dfrac{5}{2}B}\times 100 \\
\end{align}$
In the above relation, B will be cancelled out from the numerator and denominator.
$\begin{align}
  & \dfrac{2}{5}\times 100 \\
 & =40 \\
\end{align}$
From the above solution, we have found that B is 40% of A + B.
Hence, B is 40% of A + B.

Note: Instead of writing A + B in terms of B we can also write A + B in terms of A but then we have to write B in terms of A too.
From the above solution, we have found the relation between A and B as:
$A=\dfrac{3}{2}B$
Writing B in terms of A we get,
$B=\dfrac{2}{3}A$
Writing A + B in terms of A we get,
$\begin{align}
  & A+B=A+\dfrac{2}{3}A \\
 & \Rightarrow A+B=\dfrac{5}{3}A \\
\end{align}$
Now, finding B is what percent of A + B we get,
$\begin{align}
  & \dfrac{B}{A+B}\times 100 \\
 & =\dfrac{\dfrac{2}{3}A}{\dfrac{5}{3}A}\times 100 \\
 & =\dfrac{2}{5}\times 100 \\
 & =40 \\
\end{align}$
 Hence, we are getting the same percentage as we have solved above.