What percent decrease in salaries would exactly cancel out the 20 percent increase ?

Options

A. A) (16 + 2/3) %
B. B) (15 + 2/3)%
C. C) (14 +1/3)%
D. D) (13 + 4/5)%

Answer

To solve the problem of determining what percent decrease in salaries would exactly cancel out a 20 percent increase, we can follow these steps:

### Step 1: Define the Original Salary
Let's assume the original salary is \( S = 100 \) (this makes calculations easier).

### Step 2: Calculate the New Salary After 20% Increase
When the salary is increased by 20%, the new salary can be calculated as follows:
\[ \text{New Salary} = S + (20\% \text{ of } S) = S + 0.20 \times S = 100 + 20 = 120 \]

### Step 3: Determine the Amount to Decrease to Return to Original Salary
To find out how much we need to decrease the new salary (120) to return to the original salary (100), we calculate:
\[ \text{Decrease} = \text{New Salary} - \text{Original Salary} = 120 - 100 = 20 \]

### Step 4: Calculate the Percentage Decrease
Now, to find the percentage decrease, we use the formula:
\[ \text{Percentage Decrease} = \left( \frac{\text{Decrease}}{\text{New Salary}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Decrease} = \left( \frac{20}{120} \right) \times 100 \]

### Step 5: Simplify the Calculation
Calculating the fraction:
\[ \frac{20}{120} = \frac{1}{6} \]
Now, multiplying by 100:
\[ \text{Percentage Decrease} = \frac{1}{6} \times 100 = 16.67\% \]

### Final Result
Thus, the percentage decrease required to cancel out the 20% increase is approximately:
\[ \text{Percentage Decrease} = 16.67\% \]