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Sagot :
Sure, let's break down the problem to find the total gain or loss percentage step by step:
1. Selling Price of Each Article:
Each article is sold for Rs. 325.
2. Gain and Loss Percentages:
The man gains [tex]\( \frac{81}{3}\% = 27\% \)[/tex] on one article and loses [tex]\( \frac{81}{3}\% = 27\% \)[/tex] on the other article.
3. Calculating the Cost Price for Each Article:
- Gain Calculation:
Gain percentage is 27%, which in decimal form is [tex]\( \frac{27}{100} = 0.27 \)[/tex].
We use the formula for selling price in the case of gain:
[tex]\[ \text{Selling Price} = \text{Cost Price} \times (1 + \text{Gain Decimal}) \][/tex]
Rearrange it to find the Cost Price:
[tex]\[ \text{Cost Price} = \frac{\text{Selling Price}}{1 + \text{Gain Decimal}} = \frac{325}{1 + 0.27} \approx 255.91 \text{ Rs} \][/tex]
- Loss Calculation:
Loss percentage is 27%, which in decimal form is [tex]\( \frac{27}{100} = 0.27 \)[/tex].
We use the formula for selling price in the case of loss:
[tex]\[ \text{Selling Price} = \text{Cost Price} \times (1 - \text{Loss Decimal}) \][/tex]
Rearrange it to find the Cost Price:
[tex]\[ \text{Cost Price} = \frac{\text{Selling Price}}{1 - \text{Loss Decimal}} = \frac{325}{1 - 0.27} \approx 445.21 \text{ Rs} \][/tex]
4. Total Cost Price:
The total cost price for both articles is:
[tex]\[ 255.91 \text{ Rs} + 445.21 \text{ Rs} = 701.11 \text{ Rs} \][/tex]
5. Total Selling Price:
The total selling price for both articles is:
[tex]\[ 325 \text{ Rs} + 325 \text{ Rs} = 650 \text{ Rs} \][/tex]
6. Total Gain or Loss:
To determine if there's a gain or loss:
[tex]\[ \text{Total Gain/Loss} = \text{Total Selling Price} - \text{Total Cost Price} = 650 \text{ Rs} - 701.11 \text{ Rs} = -51.11 \text{ Rs} \][/tex]
Since the result is negative, it indicates a loss.
7. Total Gain or Loss Percentage:
To find the total gain or loss percentage:
[tex]\[ \text{Total Gain/Loss Percentage} = \left( \frac{\text{Total Gain/Loss}}{\text{Total Cost Price}} \right) \times 100 \][/tex]
Plugging in the values:
[tex]\[ \text{Total Gain/Loss Percentage} = \left( \frac{-51.11}{701.11} \right) \times 100 \approx -7.29\% \][/tex]
So, the man experiences an overall loss of approximately [tex]\( 7.29\% \)[/tex].
Therefore, the correct answer is none of the options listed since the options don't match the calculation result.
1. Selling Price of Each Article:
Each article is sold for Rs. 325.
2. Gain and Loss Percentages:
The man gains [tex]\( \frac{81}{3}\% = 27\% \)[/tex] on one article and loses [tex]\( \frac{81}{3}\% = 27\% \)[/tex] on the other article.
3. Calculating the Cost Price for Each Article:
- Gain Calculation:
Gain percentage is 27%, which in decimal form is [tex]\( \frac{27}{100} = 0.27 \)[/tex].
We use the formula for selling price in the case of gain:
[tex]\[ \text{Selling Price} = \text{Cost Price} \times (1 + \text{Gain Decimal}) \][/tex]
Rearrange it to find the Cost Price:
[tex]\[ \text{Cost Price} = \frac{\text{Selling Price}}{1 + \text{Gain Decimal}} = \frac{325}{1 + 0.27} \approx 255.91 \text{ Rs} \][/tex]
- Loss Calculation:
Loss percentage is 27%, which in decimal form is [tex]\( \frac{27}{100} = 0.27 \)[/tex].
We use the formula for selling price in the case of loss:
[tex]\[ \text{Selling Price} = \text{Cost Price} \times (1 - \text{Loss Decimal}) \][/tex]
Rearrange it to find the Cost Price:
[tex]\[ \text{Cost Price} = \frac{\text{Selling Price}}{1 - \text{Loss Decimal}} = \frac{325}{1 - 0.27} \approx 445.21 \text{ Rs} \][/tex]
4. Total Cost Price:
The total cost price for both articles is:
[tex]\[ 255.91 \text{ Rs} + 445.21 \text{ Rs} = 701.11 \text{ Rs} \][/tex]
5. Total Selling Price:
The total selling price for both articles is:
[tex]\[ 325 \text{ Rs} + 325 \text{ Rs} = 650 \text{ Rs} \][/tex]
6. Total Gain or Loss:
To determine if there's a gain or loss:
[tex]\[ \text{Total Gain/Loss} = \text{Total Selling Price} - \text{Total Cost Price} = 650 \text{ Rs} - 701.11 \text{ Rs} = -51.11 \text{ Rs} \][/tex]
Since the result is negative, it indicates a loss.
7. Total Gain or Loss Percentage:
To find the total gain or loss percentage:
[tex]\[ \text{Total Gain/Loss Percentage} = \left( \frac{\text{Total Gain/Loss}}{\text{Total Cost Price}} \right) \times 100 \][/tex]
Plugging in the values:
[tex]\[ \text{Total Gain/Loss Percentage} = \left( \frac{-51.11}{701.11} \right) \times 100 \approx -7.29\% \][/tex]
So, the man experiences an overall loss of approximately [tex]\( 7.29\% \)[/tex].
Therefore, the correct answer is none of the options listed since the options don't match the calculation result.
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