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
By selling an article for Rs. 2,200, a profit of 10% is earned. If the same article is sold for Rs. 2,600, then what will be the gain percentage?
By selling an article for Rs. 640, a person loses 15% of its selling price. At what price (in Rs.) should he sell it to gain 15% on its cost price?
The selling prices of articles A and B are the same. A is sold at a profit of 28 percent and B is sold at a loss of 24 percent. If the total selling price of the both articles is Rs. 48640, then what is the cost price of A and B, respectively ?
The cost price of an article is Rs. 2800. Profit as a percentage of selling price is 20 percent. What is the actual profit (in Rs.) ?
A trader bought 640 kg of rice. He sold a part of rice at 20% profit and the rest at 5% loss. He earned a profit of 15% in the entire transaction. What is the quantity (in kg) of rice that he sold at 5% loss?
