Alright, let's solve this step by step:
### Step 1: Determine the cost price of the articles sold at a loss.
The man bought articles for ₹15,000. He sold [tex]\( \frac{1}{3} \)[/tex] of the articles at a loss of 5%.
[tex]\[
\text{Cost price of articles sold at a loss} = \frac{1}{3} \times 15000 = ₹5000
\][/tex]
### Step 2: Calculate the selling price of the articles sold at a loss.
He sold them at a 5% loss. To find the selling price:
[tex]\[
\text{Selling price} = \text{Cost price} \times (1 - \text{loss percentage})
\][/tex]
[tex]\[
\text{Selling price} = 5000 \times (1 - \frac{5}{100}) = 5000 \times 0.95 = ₹4750
\][/tex]
### Step 3: Calculate the total selling price required for an 8% net gain.
To achieve an 8% net gain on the total cost price of ₹15,000:
[tex]\[
\text{Total selling price required} = \text{Total cost price} \times (1 + \text{net gain percentage})
\][/tex]
[tex]\[
\text{Total selling price required} = 15000 \times (1 + \frac{8}{100}) = 15000 \times 1.08 = ₹16200
\][/tex]
### Step 4: Determine the cost price of the remaining articles.
Since he sold [tex]\( \frac{1}{3} \)[/tex] of the articles, the remaining cost price is:
[tex]\[
\text{Cost price of remaining articles} = 15000 \times (1 - \frac{1}{3}) = 15000 \times \frac{2}{3} = ₹10000
\][/tex]
### Step 5: Calculate the required selling price of the remaining articles to achieve the total required selling price.
The total selling price required for an 8% gain is ₹16,200, out of which ₹4,750 has been achieved, so the remaining selling price needed is:
[tex]\[
\text{Remaining selling price required} = \text{Total selling price required} - \text{Selling price of articles sold at a loss}
\][/tex]
[tex]\[
\text{Remaining selling price required} = 16200 - 4750 = ₹11450
\][/tex]
### Step 6: Calculate the percentage gain required for the remaining articles.
To find the gain percentage required for the remaining articles:
[tex]\[
\text{Gain percentage} = \left( \frac{\text{Selling price of remaining articles} - \text{Cost price of remaining articles}}{\text{Cost price of remaining articles}} \right) \times 100
\][/tex]
[tex]\[
\text{Gain percentage} = \left( \frac{11450 - 10000}{10000} \right) \times 100 = \left( \frac{1450}{10000} \right) \times 100 = 14.5\%
\][/tex]
### Conclusion:
The man should sell the remaining articles at a gain of 14.5% to achieve a net gain of 8%.
