Certainly! Let's solve this problem step by step.
1. Identify Given Information:
- Selling Price with a 5% loss: Ks. 77
- Desired Profit Percentage: 26%
2. Calculate the Cost Price:
- Since the shopkeeper sold the article at a 5% loss for Ks. 77, we need to determine the cost price first.
- Loss Percentage = 5%
- Selling Price = Cost Price - Loss
- Therefore, [tex]\(77 = Cost\ Price \times (1 - \frac{5}{100})\)[/tex]
Rearranging the above formula to solve for the Cost Price, we get:
[tex]\[
Cost\ Price = \frac{77}{1 - \frac{5}{100}}
\][/tex]
Substituting the values:
[tex]\[
Cost\ Price = \frac{77}{0.95} = 81.05263157894737
\][/tex]
So, the Cost Price is approximately Ks. 81.05.
3. Determine the Desired Selling Price for a 26% Profit:
- To achieve a 26% profit, we need to calculate the selling price using the cost price.
- Profit Percentage = 26%
- Desired Selling Price = Cost Price + Profit
- Profit = Cost Price × Profit Percentage
Therefore:
[tex]\[
Desired\ Selling\ Price = Cost\ Price \times (1 + \frac{26}{100})
\][/tex]
Substituting the values:
[tex]\[
Desired\ Selling\ Price = 81.05 \times (1 + 0.26) = 81.05 \times 1.26 = 102.1263157894737
\][/tex]
Which means the shopkeeper should sell the article for approximately Ks. 102.13 to achieve a 26% profit.
Conclusion:
- The cost price of the article is approximately Ks. 81.05.
- To attain a 26% profit, the article should be sold for approximately Ks. 102.13.
