Answer :
Sure, let's solve this problem step by step.
### (i) Calculate the Marked Price of the Article
The cost price of the article is Rs. 2,000. The stationer marks up the price by 20%.
1. Mark-up Calculation:
[tex]\[ \text{Mark-up} = \text{Cost Price} \times \left(\frac{\text{Mark-up Percent}}{100}\right) \][/tex]
[tex]\[ \text{Mark-up} = 2000 \times \left(\frac{20}{100}\right) = 2000 \times 0.20 = 400 \][/tex]
2. Marked Price Calculation:
[tex]\[ \text{Marked Price} = \text{Cost Price} + \text{Mark-up} \][/tex]
[tex]\[ \text{Marked Price} = 2000 + 400 = 2400 \][/tex]
So, the marked price of the article is Rs. 2,400.
### (ii) Calculate the Selling Price After Discount
Next, we know the marked price is Rs. 2,400, and the stationer gives a discount of 10%.
1. Discount Calculation:
[tex]\[ \text{Discount} = \text{Marked Price} \times \left(\frac{\text{Discount Percent}}{100}\right) \][/tex]
[tex]\[ \text{Discount} = 2400 \times \left(\frac{10}{100}\right) = 2400 \times 0.10 = 240 \][/tex]
2. Selling Price Calculation:
[tex]\[ \text{Selling Price} = \text{Marked Price} - \text{Discount} \][/tex]
[tex]\[ \text{Selling Price} = 2400 - 240 = 2160 \][/tex]
So, the selling price of the article after the discount is Rs. 2,160.
### (iii) Calculate the Profit Percentage
Finally, we need to find the profit percentage. The profit is the difference between the selling price and the cost price.
1. Profit Calculation:
[tex]\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \][/tex]
[tex]\[ \text{Profit} = 2160 - 2000 = 160 \][/tex]
2. Profit Percentage Calculation:
[tex]\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100 \][/tex]
[tex]\[ \text{Profit Percentage} = \left(\frac{160}{2000}\right) \times 100 = 0.08 \times 100 = 8\% \][/tex]
Therefore, the profit percentage is 8%.
### (i) Calculate the Marked Price of the Article
The cost price of the article is Rs. 2,000. The stationer marks up the price by 20%.
1. Mark-up Calculation:
[tex]\[ \text{Mark-up} = \text{Cost Price} \times \left(\frac{\text{Mark-up Percent}}{100}\right) \][/tex]
[tex]\[ \text{Mark-up} = 2000 \times \left(\frac{20}{100}\right) = 2000 \times 0.20 = 400 \][/tex]
2. Marked Price Calculation:
[tex]\[ \text{Marked Price} = \text{Cost Price} + \text{Mark-up} \][/tex]
[tex]\[ \text{Marked Price} = 2000 + 400 = 2400 \][/tex]
So, the marked price of the article is Rs. 2,400.
### (ii) Calculate the Selling Price After Discount
Next, we know the marked price is Rs. 2,400, and the stationer gives a discount of 10%.
1. Discount Calculation:
[tex]\[ \text{Discount} = \text{Marked Price} \times \left(\frac{\text{Discount Percent}}{100}\right) \][/tex]
[tex]\[ \text{Discount} = 2400 \times \left(\frac{10}{100}\right) = 2400 \times 0.10 = 240 \][/tex]
2. Selling Price Calculation:
[tex]\[ \text{Selling Price} = \text{Marked Price} - \text{Discount} \][/tex]
[tex]\[ \text{Selling Price} = 2400 - 240 = 2160 \][/tex]
So, the selling price of the article after the discount is Rs. 2,160.
### (iii) Calculate the Profit Percentage
Finally, we need to find the profit percentage. The profit is the difference between the selling price and the cost price.
1. Profit Calculation:
[tex]\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \][/tex]
[tex]\[ \text{Profit} = 2160 - 2000 = 160 \][/tex]
2. Profit Percentage Calculation:
[tex]\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100 \][/tex]
[tex]\[ \text{Profit Percentage} = \left(\frac{160}{2000}\right) \times 100 = 0.08 \times 100 = 8\% \][/tex]
Therefore, the profit percentage is 8%.
