Let's solve the problem step-by-step.
1. Initial Quantity: Let's denote the original quantity as [tex]\( Q \)[/tex]. We can assume [tex]\( Q = 100 \)[/tex] for simplicity, i.e., we start with 100 units.
2. Decreasing the Quantity by 20%:
- A decrease of 20% means we multiply the original quantity by [tex]\( 1 - 0.20 = 0.80 \)[/tex].
- Therefore, the new quantity after decreasing by 20% is [tex]\( 100 \times 0.80 = 80 \)[/tex].
3. Increasing the Results by 10%:
- To increase the new quantity (which is 80) by 10%, we multiply it by [tex]\( 1 + 0.10 = 1.10 \)[/tex].
- So, the new quantity after increasing by 10% is [tex]\( 80 \times 1.10 = 88 \)[/tex].
4. Decreasing Compared to the Original Quantity:
- The original quantity was 100 units, and the final quantity after these percent changes is 88 units.
- To find the change, subtract the final quantity from the original quantity: [tex]\( 100 - 88 = 12 \)[/tex].
5. Finding the Percentage Change:
- To find the percentage change with respect to the original quantity, use the formula:
[tex]\[
\text{Percentage Change} = \left( \frac{\text{Change in Quantity}}{\text{Original Quantity}} \right) \times 100
\][/tex]
- Substituting the values, we get:
[tex]\[
\text{Percentage Change} = \left( \frac{-12}{100} \right) \times 100 = -12\%
\][/tex]
Therefore, the original quantity is decreased by [tex]\( 12\% \)[/tex].
