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To solve the problem, we need to determine the selling price, cost price, and the gain percent for the cassettes. Here is the step-by-step solution:
### Step 1: Define the Given Information
- Number of cassettes sold: 250
- Gain is equal to the selling price of 25 cassettes.
### Step 2: Determine the Cost Price (CP) and Selling Price (SP)
- Let the selling price of one cassette be denoted as [tex]\( sp \)[/tex].
- Therefore, the selling price of 250 cassettes is [tex]\( 250 \times sp \)[/tex].
### Step 3: Calculate the Gain and Relate it to the Selling Price
- The gain on selling 250 cassettes is given to be equal to the selling price of 25 cassettes, which is [tex]\( 25 \times sp \)[/tex].
### Step 4: Calculate the Total Cost Price
- Gain on selling 250 cassettes can be expressed as:
[tex]\[ \text{Gain} = \text{Selling Price of 250 cassettes} - \text{Cost Price of 250 cassettes} \][/tex]
[tex]\[ 25 \times sp = 250 \times sp - \text{Cost Price of 250 cassettes} \][/tex]
- Rearrange to find the Cost Price of 250 cassettes:
[tex]\[ \text{Cost Price of 250 cassettes} = 250 \times sp - 25 \times sp \][/tex]
[tex]\[ = 225 \times sp \][/tex]
### Step 5: Determine Cost Price and Selling Price per Cassette
- Let's denote the selling price of 25 cassettes as [tex]\( \$25 \)[/tex].
- Therefore, [tex]\( sp = \frac{25}{25} = 1 \)[/tex] dollar per cassette.
- The cost price of 250 cassettes is:
[tex]\[ \text{Cost Price of 250 cassettes} = 225 \times 1 = \$225 \][/tex]
- The cost price of one cassette:
[tex]\[ \text{Cost Price per cassette} = \frac{225}{250} = 0.9 \text{ dollars} \][/tex]
- The selling price of one cassette:
[tex]\[ \text{Selling Price per cassette} = 1 \text{ dollar} \][/tex]
### Step 6: Calculate Gain Percent
- Gain per cassette:
[tex]\[ \text{Gain per cassette} = \text{Selling Price per cassette} - \text{Cost Price per cassette} \][/tex]
[tex]\[ = 1 - 0.9 = 0.1 \text{ dollars} \][/tex]
- Gain percent:
[tex]\[ \text{Gain Percent} = \frac{\text{Gain per cassette}}{\text{Cost Price per cassette}} \times 100 \][/tex]
[tex]\[ = \frac{0.1}{0.9} \times 100 \approx 11.11\% \][/tex]
### Summary of Results:
- Cost Price of 250 cassettes: \[tex]$225 - Cost Price per cassette: \$[/tex]0.9
- Selling Price per cassette: \$1
- Gain Percent: 11.11%
Thus, we have found the step-by-step solution to the problem, determining the cost price per cassette, selling price per cassette, and the gain percent.
### Step 1: Define the Given Information
- Number of cassettes sold: 250
- Gain is equal to the selling price of 25 cassettes.
### Step 2: Determine the Cost Price (CP) and Selling Price (SP)
- Let the selling price of one cassette be denoted as [tex]\( sp \)[/tex].
- Therefore, the selling price of 250 cassettes is [tex]\( 250 \times sp \)[/tex].
### Step 3: Calculate the Gain and Relate it to the Selling Price
- The gain on selling 250 cassettes is given to be equal to the selling price of 25 cassettes, which is [tex]\( 25 \times sp \)[/tex].
### Step 4: Calculate the Total Cost Price
- Gain on selling 250 cassettes can be expressed as:
[tex]\[ \text{Gain} = \text{Selling Price of 250 cassettes} - \text{Cost Price of 250 cassettes} \][/tex]
[tex]\[ 25 \times sp = 250 \times sp - \text{Cost Price of 250 cassettes} \][/tex]
- Rearrange to find the Cost Price of 250 cassettes:
[tex]\[ \text{Cost Price of 250 cassettes} = 250 \times sp - 25 \times sp \][/tex]
[tex]\[ = 225 \times sp \][/tex]
### Step 5: Determine Cost Price and Selling Price per Cassette
- Let's denote the selling price of 25 cassettes as [tex]\( \$25 \)[/tex].
- Therefore, [tex]\( sp = \frac{25}{25} = 1 \)[/tex] dollar per cassette.
- The cost price of 250 cassettes is:
[tex]\[ \text{Cost Price of 250 cassettes} = 225 \times 1 = \$225 \][/tex]
- The cost price of one cassette:
[tex]\[ \text{Cost Price per cassette} = \frac{225}{250} = 0.9 \text{ dollars} \][/tex]
- The selling price of one cassette:
[tex]\[ \text{Selling Price per cassette} = 1 \text{ dollar} \][/tex]
### Step 6: Calculate Gain Percent
- Gain per cassette:
[tex]\[ \text{Gain per cassette} = \text{Selling Price per cassette} - \text{Cost Price per cassette} \][/tex]
[tex]\[ = 1 - 0.9 = 0.1 \text{ dollars} \][/tex]
- Gain percent:
[tex]\[ \text{Gain Percent} = \frac{\text{Gain per cassette}}{\text{Cost Price per cassette}} \times 100 \][/tex]
[tex]\[ = \frac{0.1}{0.9} \times 100 \approx 11.11\% \][/tex]
### Summary of Results:
- Cost Price of 250 cassettes: \[tex]$225 - Cost Price per cassette: \$[/tex]0.9
- Selling Price per cassette: \$1
- Gain Percent: 11.11%
Thus, we have found the step-by-step solution to the problem, determining the cost price per cassette, selling price per cassette, and the gain percent.
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