A shopkeeper marks up his goods by 40% and offers a discount of 10%. What is his final profit percentage?
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Solution and Explanation
Step 1: Understanding the problem.
The shopkeeper marks up the goods by 40% and gives a discount of 10%. We need to calculate the final profit percentage.
Step 2: Calculating the Cost Price (C.P.) and Selling Price (S.P.).
Let the cost price of the item be \( C \).
- Marked Price (M.P.) = \( C + 40% \, \text{of} \, C = C \times 1.40 \).
- The shopkeeper offers a 10% discount on the marked price, so the selling price is: \[ \text{Selling Price} = M.P. \times (1 - 0.10) = C \times 1.40 \times 0.90 = C \times 1.26 \]
Step 3: Finding the Profit Percentage.
Profit = Selling Price - Cost Price = \( C \times 1.26 - C = C \times 0.26 \).
Profit Percentage = \( \frac{\text{Profit}}{\text{Cost Price}} \times 100 = \frac{C \times 0.26}{C} \times 100 = 26% \).
Step 4: Conclusion.
The final profit percentage is 36%.
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