A seller marks their goods 28% above the cost price. On customer demand, they offer a 25% reduction on the bills. What percentage of profit or loss does the seller make?
To determine the profit or loss percentage, let's follow the steps of the transaction:
Step 1: Assume a Cost Price (CP)
Let the Cost Price (CP) be $100$.
Step 2: Calculate the Marked Price (MP)
The seller marks the goods $28\%$ above the cost price.
$$MP = CP + 28\% \text{ of } CP$$
$$MP = 100 + (0.28 \times 100) = \mathbf{128}$$
Step 3: Calculate the Selling Price (SP)
The seller offers a $25\%$ reduction (discount) on the bill (the marked price).
$$SP = MP - 25\% \text{ of } MP$$
$$SP = 128 - (0.25 \times 128)$$
$$SP = 128 - 32 = \mathbf{96}$$
Step 4: Determine Profit or Loss
Now, compare the Selling Price (SP) with the Cost Price (CP):
CP = $100$
SP = $96$
Since the Selling Price is less than the Cost Price, the seller makes a loss.
$$Loss = CP - SP = 100 - 96 = 4$$
Step 5: Calculate Percentage
$$Loss\% = \left( \frac{Loss}{CP} \right) \times 100$$
$$Loss\% = \left( \frac{4}{100} \right) \times 100 = \mathbf{4\%}$$
Final Answer:
The seller makes a 4% loss.
Important Questions from Profit and Loss
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A shopkeeper bought an item for Rs. 4,500 and sold it at a loss of 5%. From this money, he bought another item and sold it at a profit of 10%. What is his overall profit?
A man sells two articles at Rs. 9,180 each. He gains 8% on one article and loses 15% on the other. His overall profit or loss is:
A shopkeeper selling an article for ₹46 loses 8%. In order to gain 6%, what should be the selling price of the article?
Rahul purchased 80 items from the market. 25% items of the total items were defective and the remaining items were sold at 50% profit. What will be the overall profit percentage?
