Question

Fill in the blanks to make the statement true: If $A$ is increased by $20\%$, it equals $B$. If $B$ is decreased by $50\%$, it equals $C$. Then _______ $\%$ of $A$ is equal to $C$.

Answer 1

Form equations from the given information

Given, $A$ is increased by $20\%$, and is equal to $B$, so $B=A+\frac{20}{100}A$ $...\left(1\right)$

Also, it is given that if $B$ is decreased by $50\%$, it equals $C$, so $C=B-\frac{50}{100}B$ $...\left(2\right)$

Substitute the value of $B$ from equation $\left(1\right)$ in equation $\left(2\right)$, we get

$$\begin{gathered} \Rightarrow C=(A+\frac{20}{100}A)-\frac{50}{100}(A+\frac{20}{100}A) \\ \Rightarrow C=(A+\frac{1}{5}A)-\frac{1}{2}(A+\frac{1}{5}A) \\ \Rightarrow C=\left(\frac{5A+A}{5}\right)-\frac{1}{2}\left(\frac{5A+A}{5}\right) \\ \Rightarrow C=\frac{6A}{5}-\frac{3A}{5} \\ \Rightarrow C=\frac{3}{5}A \end{gathered}$$

So, $C$ is $\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$ of $A$.

Now, convert this into percentage by multiplying the value by $100$,

$$\begin{gathered} \Rightarrow C=\frac{3}{5}\times 100\mathrm{of}A \\ \Rightarrow C=60\%\text{of}A \end{gathered}$$

Therefore, $60\%$ of $A$ is equal to $C$.