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
Rohit buys 8 pens and 4 pencils for Rs. 2400. He sells pencils at a profit of 20 percent and pens at the loss of 10 percent. If his overall profit is Rs. 240, then what is the sum of the cost price of one pen and one pencil?
A man sells a car to his friend at the loss of 10 %; who in return sells it for Rs. 54000 making a profit of 20 %. What was the initial value of the car?
An article was sold at a loss of 24%. If it were sold for Rs. 1,596 more, then there would have been a gain of 18%, The cost price of the article is:
The cost price of an article is Rs.6,450. If it sold at a profit 16%, how much would be its selling price?
If the selling price of 7 articles is equal to the cost price of 6 articles, then what is the percentage loss?
