Question

Rahim's salary was reduced by 10% and then the reduced salary was increased by 10%. What was his ultimate loss?

• A. 0%
• B. 1%
• C. 10%
• D. 5%

Hint:

When a quantity is first decreased and then increased by the same percentage, the final value will always be less than the initial value. The difference is due to the decrease being larger than the increase in percentage terms.

Answer 1

The Correct Option is B

Let Rahim's initial salary be \( S \).
- First, his salary is reduced by 10%, so his reduced salary is: \[ S' = S - 0.10S = 0.90S \] - Then, the reduced salary is increased by 10%, so the new salary is: \[ S'' = 0.90S + 0.10 \times 0.90S = 0.90S \times 1.10 = 0.99S \] Thus, his final salary is 99% of his initial salary, which means there is a 1% loss. Therefore, the ultimate loss is 1%.

Answer 2

Let Rahim’s original salary be ₹100 (assuming a base value for easier calculation).

Step 1: Apply the 10% reduction
10% of ₹100 = ₹10
Reduced salary = ₹100 - ₹10 = ₹90

Step 2: Apply a 10% increase on the reduced salary
10% of ₹90 = ₹9
Increased salary = ₹90 + ₹9 = ₹99

Step 3: Calculate the net change
Original salary = ₹100
Final salary = ₹99
Loss = ₹100 - ₹99 = ₹1

Step 4: Calculate the percentage loss
(₹1 / ₹100) × 100 = 1%

Conclusion:
Rahim's ultimate loss in salary is 1%.