What will be the input based on the output?

Question

A = 1.0 B = 1.0

C = A / (1-(B/100)) This will give an output as 1.01

What will be the output when A and C are only given? A = 1.0; B = ?; C = 1.01;

1.10 = 1.0 / (1-(? / 100))

What is the answer for B?

Answer: The answer for be is 1.0, But how the calculation work? Please explain.

Answer 1

This is for $C=1.10$, if you want $C=1.01$ you can fill it in.

We have to solve $1.10=\frac{1.0}{1-\frac{B}{100}}$.

We can lift $1.0$ to the other side, so $\frac{1.0}{1.10}=1-\frac{b}{100}$.

Then we can get $1$ to the left so $1-\frac{1.0}{1.10} =\frac{b}{100}$.

And then: $100 -\frac{100}{1.1} = b$.

So $$b=9.090909$$

Answer 2

We have $1,1= \frac{1}{1-\frac{B}{100}}$. Can you proceed ?

Answer 3

You can re-arrange the equation to find an expression for $B$ in terms of $A$ and $C$.

Starting from

$C = \frac{A}{1-\frac{B}{100}}$

First multiply both sides of the equation by $1-\frac{B}{100}$:

$C\left(1-\frac{B}{100} \right) = A$

then divide both sides by $C$:

$1-\frac{B}{100} = \frac{A}{C}$

Subtract $1$ from both sides:

$-\frac{B}{100}=\frac{A}{C}-1$

Multiply both sides by $-100$:

$B = 100 \left( 1-\frac{A}{C} \right)$