The strength of a school increases and decreases in every alternate year by 10%. It started with increase in 2000. Then the strength of the school in 2003 as compared to that in 2000 was

Options

A. increased by 8.9
B. decreased 8.9
C. increased by 9.8
D. decreased 9.8

Answer

To solve the problem step-by-step, we need to track the changes in the strength of the school from the year 2000 to 2003, considering the alternating increases and decreases of 10%.

### Step-by-Step Solution:

1. **Initial Strength in 2000**:
Let's assume the initial strength of the school in the year 2000 is 100.

2. **Strength in 2000 (after increase)**:
The strength increases by 10%.
\[ \text{Increase} = 10\% \text{ of } 100 = 10 \]
\[ \text{New Strength} = 100 + 10 = 110 \]

3. **Strength in 2001 (after decrease)**:
The strength decreases by 10% of the new strength (110).
\[ \text{Decrease} = 10\% \text{ of } 110 = 11 \]
\[ \text{New Strength} = 110 - 11 = 99 \]

4. **Strength in 2002 (after increase)**:
The strength increases again by 10% of the new strength (99).
\[ \text{Increase} = 10\% \text{ of } 99 = 9.9 \]
\[ \text{New Strength} = 99 + 9.9 = 108.9 \]

5. **Strength in 2003 (after decrease)**:
The strength decreases by 10% of the new strength (108.9).
\[ \text{Decrease} = 10\% \text{ of } 108.9 = 10.89 \]
\[ \text{New Strength} = 108.9 - 10.89 = 98.01 \]

6. **Comparison of Strength in 2003 to 2000**:
Now, we need to find the percentage change from the original strength (100) to the strength in 2003 (98.01).
\[ \text{Change} = 98.01 - 100 = -1.99 \]
\[ \text{Percentage Change} = \left(\frac{-1.99}{100}\right) \times 100 = -1.99\% \]

### Final Result:
The strength of the school in 2003 compared to that in 2000 is a decrease of approximately **1.99%**.

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