A number is increased first by `10%` and then it is decreased by `10%` .What is the percentage change in the number ? (a)`11%` increase (b)No change (c)`1%` decrease (d)`11%` decrease

Options

A. `11%` increase
B. No change
C. `1%` decrease
D. `11%` decrease

Answer

To solve the problem step by step, we will follow the changes made to the number and calculate the overall percentage change.

**Step 1: Let the initial number be 100.**
- This is a convenient choice because it makes percentage calculations straightforward.

**Step 2: Increase the number by 10%.**
- Calculation:
\[ \text{Increased number} = 100 + (10\% \text{ of } 100) = 100 + 10 = 110 \]

**Step 3: Decrease the new number (110) by 10%.**
- Calculation:
\[ \text{Decreased number} = 110 - (10\% \text{ of } 110) = 110 - 11 = 99 \]

**Step 4: Calculate the overall change from the original number (100) to the final number (99).**
- Change in number:
\[ \text{Change} = 99 - 100 = -1 \]

**Step 5: Calculate the percentage change.**
- Percentage change formula:
\[ \text{Percentage change} = \left(\frac{\text{Change}}{\text{Original number}}\right) \times 100 = \left(\frac{-1}{100}\right) \times 100 = -1\% \]

Thus, the final answer is that there is a **1% decrease** in the number.