Question

The salary of a worker is first increased by 5% and then it is decreased by 5%. What is the change in his salary?

• A. Decrease in salary 0-25%
• B. Increase in salary 0-50%
• C. No change in salary
• D. Decrease in salary 0-50%

Hint:

When a salary is first increased and then decreased by the same percentage, the final salary will be slightly lower than the original salary due to the compound effect of the percentage changes.

Answer 1

The Correct Option is A

Step 1: Let the initial salary be \( S \).
The worker's salary is first increased by 5%, so the new salary after the increase is:S_new = S + 0.05S = 1.05S Step 2: Then, the salary is decreased by 5% from the increased salary.
Now, the new salary after the 5% decrease is:S_final = 1.05S - 0.05(1.05S) = 1.05S(1 - 0.05) = 1.05S × 0.95 = 0.9975S Step 3: Calculate the change in salary.
The final salary is 0.9975S, which is slightly less than the initial salary S. The percentage change in salary is:Percentage change = (S_final - S) / S × 100 = (0.9975S - S) / S × 100 = -0.25% This shows a decrease of 0.25%. 
Step 4: Conclusion.
The salary decreases by 0.25%, so the correct answer is (1) Decrease in salary 0.25%.