What percent decrease in salaries would exactly cancel the 20 percent increase?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(16\frac{2}{3}\)%
The decrease is worked out on the raised salary, not on the original one, so it is a smaller percentage than the 20% rise.
Assuming the original salary to be 100:
Salary after the 20% rise \(=120\)
Fall needed to bring it back to 100 \(=20\)
Decrease \(\displaystyle =\frac{20}{120}\times100=16\frac{2}{3}\%\)
Tip: To cancel a rise of \(r\%\), the decrease is \(\displaystyle \frac{r}{100+r}\times100\%\). The base has grown, so the cut is always smaller than the rise.