Calculating the Selling Price After Discounts and Loss
Let the Cost Price (CP) of the item be \(C\). The trader marked the price 40% above the cost price. So, the Marked Price (MP) is:
\(MP\) = \(C + (40\% \text{ of } C)\)
\(MP\) = \(C + 0.40C = 1.40C\)
The trader allowed two successive discounts: 20% and 25%. The price after the first discount (20%) is:
\(Price after 1st discount\) = \(MP \times (1 - 0.20)\)
\(Price after 1st discount\) = \(MP \times 0.80\)
The final Selling Price (SP) after the second discount (25%) is:
\(SP\) = (\(Price after 1st discount\)) \(\times (1 - 0.25)\)
\(SP\) = (\(MP \times 0.80\)) \(\times 0.75\)
\(SP\) = \(MP \times (0.80 \times 0.75)\)
\(SP\) = \(MP \times 0.60\)
Now, substitute the expression for MP in terms of C:
\(SP\) = \((1.40C) \times 0.60\)
\(SP\) = \(0.84C\)
The trader incurred a loss of ₹224. The formula for loss is:
\(Loss\) = \(CP - SP\)
Given Loss = ₹224:
\(224 = C - 0.84C\)
\(224 = 0.16C\)
Solve for the Cost Price (C):
\(C = \frac{224}{0.16}\)
\(C = 1400\)
So, the Cost Price is ₹1400.
Determining the Final Selling Price
Now, calculate the Selling Price (SP) using the calculated Cost Price:
\(SP\) = \(0.84C\)
\(SP\) = \(0.84 \times 1400\)
\(SP\) = \(1176\)
The selling price of the item is ₹1,176.
Similar Questions
A trader marks an article 25% above its cost price. He allows a discount of 10% on the marked price. After giving the discount, he makes a profit of ₹180 on the article. What is the cost price of the article?
A shopkeeper marks a product 75% above cost price and offers two successive discounts of 30% and 40%. What is the profit or loss percentage?
A trader buys 187 pens at ₹23 each. During transportation, 7 pens get damaged and cannot be sold. He sells the remaining pens at ₹27 each. Find his profit percentage. (rounded off to one decimal place)
A dealer buys a table for ₹2,750. He first marks it up by 28%, then allows a 12% discount to a customer. If the customer also pays 5% GST on the selling price, find the profit percentage (excluding GST) made by the dealer.
- During a sale, 50% of the goods are sold at a 49% profit, 32% of the remaining goods are sold at a 45% profit and the still remaining goods are sold at a loss of 15%. If there is an overall profit of x%, then what is the value of x?
- During a sale, 55% of the goods are sold at a 41% profit, 20% of the remaining goods are sold at a 19% profit and the rest are sold at a 21% loss. If there is an overall profit of x%, then what is the value of x?
- During a sale, 40% of the goods are sold at a 44% profit, 25% of the remaining goods are sold at a 29% profit and the rest are sold at a 39% loss. If there is an overall profit of x%, then what is the value of x?
- The marked price of an item is 10% higher than the cost price and a discount of 10% is given on the marked price. What is the percentage gain or loss to the business owner in this sale?
- An article was sold for ₹ 576 when its cost price was ₹ 600. What is the percentage loss?
- The rate of discount on an article whose marked price is ₹ 170 and selling price is ₹ 130 is:
Important Questions from Profit and Loss
Ram bought a chair at 35% discount on its market price, Had Ram got no discount, he would have had to pay ₹245 more. How much did Ram pay for the chair?
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?
