Sure, let's break down the problem step-by-step to find the answer.
1. Define Jack's Salary: Choose an arbitrary value for simplicity. We can say Jack's salary is 100 units.
2. Calculate Michael's Salary: Since Michael's salary is a 20% increase over Jack's salary:
- Calculate 20% of Jack's salary: [tex]\( \text{20% of 100 units} = 20 \)[/tex] units.
- Add this to Jack's salary to get Michael's salary: [tex]\( 100 \text{ units} + 20 \text{ units} = 120 \text{ units} \)[/tex].
3. Calculate the difference in salaries: The difference between Michael's and Jack's salary is:
- Difference = Michael's salary - Jack's salary = [tex]\( 120 \text{ units} - 100 \text{ units} = 20 \text{ units} \)[/tex].
4. Express this difference as a percentage of Michael's salary:
- Percentage = [tex]\(\left(\frac{\text{Difference}}{\text{Michael's Salary}}\right) \times 100\)[/tex]
- Substituting the values, we get: [tex]\(\left(\frac{20 \text{ units}}{120 \text{ units}}\right) \times 100 = \frac{20}{120} \times 100\)[/tex]
- Perform the division: [tex]\( \frac{20}{120} = \frac{1}{6} \)[/tex]
- Then multiply by 100 to convert it to a percentage: [tex]\( \frac{1}{6} \times 100 \approx 16.67\% \)[/tex].
Thus, Jack's salary is approximately 16.67% less than Michael's salary. The closest option is:
16.67%
