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Sagot :
Let's start by calculating the discount percentage for the laptop that originally costs \[tex]$900 and is now selling for \$[/tex]720.
1. Calculating the discount amount:
[tex]\[ \text{Discount Amount} = \text{Original Cost} - \text{Selling Price} \][/tex]
[tex]\[ \text{Discount Amount} = 900 - 720 = 180 \][/tex]
2. Calculating the discount percentage:
[tex]\[ \text{Discount Percentage} = \left( \frac{\text{Discount Amount}}{\text{Original Cost}} \right) \times 100 \][/tex]
[tex]\[ \text{Discount Percentage} = \left( \frac{180}{900} \right) \times 100 = 20\% \][/tex]
So, the discount percentage is [tex]\(20\%\)[/tex].
Next, let's complete the table with the given items, cost prices, and selling prices. We will also calculate the profit/loss and their respective percentages.
### Table Calculation Details:
1. Watch:
- Cost Price (CP): \[tex]$75 - Selling Price (SP): \$[/tex]90
- Profit (P):
[tex]\[ P = SP - CP = 90 - 75 = 15 \][/tex]
- Profit Percentage:
[tex]\[ \text{Profit \%} = \left( \frac{P}{CP} \right) \times 100 = \left( \frac{15}{75} \right) \times 100 = 20\% \][/tex]
- Loss does not apply.
2. Table:
- Cost Price (CP): \[tex]$120 - Selling Price (SP): \$[/tex]100
- Loss (L):
[tex]\[ L = CP - SP = 120 - 100 = 20 \][/tex]
- Loss Percentage:
[tex]\[ \text{Loss \%} = \left( \frac{L}{CP} \right) \times 100 = \left( \frac{20}{120} \right) \times 100 = 16.\overline{66} \% \approx 16.67\% \][/tex]
- Profit does not apply.
3. Lamp:
- Cost Price (CP): \[tex]$45 - Selling Price (SP): \$[/tex]55
- Profit (P):
[tex]\[ P = SP - CP = 55 - 45 = 10 \][/tex]
- Profit Percentage:
[tex]\[ \text{Profit \%} = \left( \frac{P}{CP} \right) \times 100 = \left( \frac{10}{45} \right) \times 100 = 22.\overline{22} \% \approx 22.22\% \][/tex]
- Loss does not apply.
4. Book:
- Cost Price (CP): \[tex]$30 - Selling Price (SP): \$[/tex]25
- Loss (L):
[tex]\[ L = CP - SP = 30 - 25 = 5 \][/tex]
- Loss Percentage:
[tex]\[ \text{Loss \%} = \left( \frac{L}{CP} \right) \times 100 = \left( \frac{5}{30} \right) \times 100 = 16.\overline{66} \% \approx 16.67\% \][/tex]
- Profit does not apply.
5. Phone:
- Cost Price (CP): \[tex]$250 - Selling Price (SP): \$[/tex]275
- Profit (P):
[tex]\[ P = SP - CP = 275 - 250 = 25 \][/tex]
- Profit Percentage:
[tex]\[ \text{Profit \%} = \left( \frac{P}{CP} \right) \times 100 = \left( \frac{25}{250} \right) \times 100 = 10\% \][/tex]
- Loss does not apply.
### Completed Table:
[tex]\[ \begin{array}{|l|c|c|c|c|c|c|} \hline \text{Item} & \text{Cost Price (CP)} & \text{Selling Price (SP)} & \text{Profit (P)} & \text{Loss (L)} & \text{Profit \%} & \text{Loss \%} \\ \hline \text{Watch} & \$75 & \$90 & 15 & 0 & 20\% & 0\% \\ \hline \text{Table} & \$120 & \$100 & 0 & 20 & 0\% & 16.67\% \\ \hline \text{Lamp} & \$45 & \$55 & 10 & 0 & 22.22\% & 0\% \\ \hline \text{Book} & \$30 & \$25 & 0 & 5 & 0\% & 16.67\% \\ \hline \text{Phone} & \$250 & \$275 & 25 & 0 & 10\% & 0\% \\ \hline \end{array} \][/tex]
1. Calculating the discount amount:
[tex]\[ \text{Discount Amount} = \text{Original Cost} - \text{Selling Price} \][/tex]
[tex]\[ \text{Discount Amount} = 900 - 720 = 180 \][/tex]
2. Calculating the discount percentage:
[tex]\[ \text{Discount Percentage} = \left( \frac{\text{Discount Amount}}{\text{Original Cost}} \right) \times 100 \][/tex]
[tex]\[ \text{Discount Percentage} = \left( \frac{180}{900} \right) \times 100 = 20\% \][/tex]
So, the discount percentage is [tex]\(20\%\)[/tex].
Next, let's complete the table with the given items, cost prices, and selling prices. We will also calculate the profit/loss and their respective percentages.
### Table Calculation Details:
1. Watch:
- Cost Price (CP): \[tex]$75 - Selling Price (SP): \$[/tex]90
- Profit (P):
[tex]\[ P = SP - CP = 90 - 75 = 15 \][/tex]
- Profit Percentage:
[tex]\[ \text{Profit \%} = \left( \frac{P}{CP} \right) \times 100 = \left( \frac{15}{75} \right) \times 100 = 20\% \][/tex]
- Loss does not apply.
2. Table:
- Cost Price (CP): \[tex]$120 - Selling Price (SP): \$[/tex]100
- Loss (L):
[tex]\[ L = CP - SP = 120 - 100 = 20 \][/tex]
- Loss Percentage:
[tex]\[ \text{Loss \%} = \left( \frac{L}{CP} \right) \times 100 = \left( \frac{20}{120} \right) \times 100 = 16.\overline{66} \% \approx 16.67\% \][/tex]
- Profit does not apply.
3. Lamp:
- Cost Price (CP): \[tex]$45 - Selling Price (SP): \$[/tex]55
- Profit (P):
[tex]\[ P = SP - CP = 55 - 45 = 10 \][/tex]
- Profit Percentage:
[tex]\[ \text{Profit \%} = \left( \frac{P}{CP} \right) \times 100 = \left( \frac{10}{45} \right) \times 100 = 22.\overline{22} \% \approx 22.22\% \][/tex]
- Loss does not apply.
4. Book:
- Cost Price (CP): \[tex]$30 - Selling Price (SP): \$[/tex]25
- Loss (L):
[tex]\[ L = CP - SP = 30 - 25 = 5 \][/tex]
- Loss Percentage:
[tex]\[ \text{Loss \%} = \left( \frac{L}{CP} \right) \times 100 = \left( \frac{5}{30} \right) \times 100 = 16.\overline{66} \% \approx 16.67\% \][/tex]
- Profit does not apply.
5. Phone:
- Cost Price (CP): \[tex]$250 - Selling Price (SP): \$[/tex]275
- Profit (P):
[tex]\[ P = SP - CP = 275 - 250 = 25 \][/tex]
- Profit Percentage:
[tex]\[ \text{Profit \%} = \left( \frac{P}{CP} \right) \times 100 = \left( \frac{25}{250} \right) \times 100 = 10\% \][/tex]
- Loss does not apply.
### Completed Table:
[tex]\[ \begin{array}{|l|c|c|c|c|c|c|} \hline \text{Item} & \text{Cost Price (CP)} & \text{Selling Price (SP)} & \text{Profit (P)} & \text{Loss (L)} & \text{Profit \%} & \text{Loss \%} \\ \hline \text{Watch} & \$75 & \$90 & 15 & 0 & 20\% & 0\% \\ \hline \text{Table} & \$120 & \$100 & 0 & 20 & 0\% & 16.67\% \\ \hline \text{Lamp} & \$45 & \$55 & 10 & 0 & 22.22\% & 0\% \\ \hline \text{Book} & \$30 & \$25 & 0 & 5 & 0\% & 16.67\% \\ \hline \text{Phone} & \$250 & \$275 & 25 & 0 & 10\% & 0\% \\ \hline \end{array} \][/tex]
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