Question

Quantity A: Net change when wages of workers were increased by 20% and then reduced by 10%.
Quantity B: Net change when wages of workers were reduced by 10% and then increased by 20%.

• A. if the quantity A is greater.
• B. if the quantity B is greater.
• C. if the two quantities A and B are equal.
• D. if comparison cannot be made from the given information.

Hint:

When calculating percentage increases and decreases, always apply the changes sequentially to the initial value and compare the final results. In cases like this, the order of operations (increase first or decrease first) doesn’t affect the final result when the percentage values are symmetric.

Answer 1

The Correct Option is C

We are given two scenarios: one where the wages of workers were increased by 20% and then reduced by 10%, and another where the wages were first reduced by 10% and then increased by 20%. Let’s analyze both cases.
Quantity A: In this case, the wages are increased by 20% and then reduced by 10%. Let the initial wage be \( W \). - After a 20% increase:
New wage = \( W \times (1 + 0.20) = W \times 1.20 \) - After a 10% reduction on the new wage:
New wage = \( W \times 1.20 \times (1 - 0.10) = W \times 1.20 \times 0.90 = W \times 1.08 \) Thus, the net change in wages is an increase of 8% (since the final wage is 1.08 times the initial wage).
Quantity B:
In this case, the wages are reduced by 10% and then increased by 20%. Let the initial wage again be \( W \).
- After a 10% reduction:
New wage = \( W \times (1 - 0.10) = W \times 0.90 \)
- After a 20% increase on the new wage:
New wage = \( W \times 0.90 \times (1 + 0.20) = W \times 0.90 \times 1.20 = W \times 1.08 \)
Thus, the net change in wages is also an increase of 8% (since the final wage is 1.08 times the initial wage).
Conclusion:
Both quantities A and B result in the same final net change of 8%, hence the two quantities are equal.
Thus, the correct answer is (3).