Let's approach this step-by-step:
1. Understanding the loss scenario:
- The selling price when the carpenter incurs a loss of 20% is $125240.
2. Calculating the Cost Price (C.P):
- Given that the selling price (S.P) is $125240 and this results in a 20% loss, we need to find the original cost price.
- Loss percent = 20%
- We know that:
[tex]\[
\text{Loss} = \text{Cost Price} \times \frac{\text{Loss Percent}}{100}
\][/tex]
[tex]\[
125240 = \text{Cost Price} - (\text{Cost Price} \times \frac{20}{100})
\][/tex]
[tex]\[
125240 = \text{Cost Price} \times (1 - 0.20)
\][/tex]
[tex]\[
125240 = \text{Cost Price} \times 0.80
\][/tex]
- Hence, the cost price (C.P) can be calculated as:
[tex]\[
\text{Cost Price} = \frac{125240}{0.80} = 156550.0
\][/tex]
3. Evaluating the new selling price scenario:
- The carpenter is now selling the same item for $125360.
- We need to determine the new profit/loss percentage based on this new selling price.
4. Calculating the new profit/loss percentage:
- New selling price (S.P) = $125360
- Cost price (C.P) = $156550.0 (calculated before)
- To find the profit or loss percentage:
[tex]\[
\text{Profit/Loss Percent} = \left(\frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}}\right) \times 100
\][/tex]
[tex]\[
\text{Profit/Loss Percent} = \left(\frac{125360 - 156550}{156550}\right) \times 100
\][/tex]
[tex]\[
\text{Profit/Loss Percent} = \left(\frac{-31190}{156550}\right) \times 100
\][/tex]
[tex]\[
\text{Profit/Loss Percent} = -0.19923347173427018 \times 100
\][/tex]
[tex]\[
\text{Profit/Loss Percent} = -19.923347173427018\%
\][/tex]
Conclusion:
By selling the item for $125360, the carpenter would incur a loss of approximately 19.92%.
