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 dishonest dealer professes to sell goods at the cost price, but uses a false weight of 900 grams instead of a kilogram. His gain percentage is:
A dishonest dealer professes to sell his goods at cost price, but uses a false weight and thus gains 25%. For 100 grams, he uses a weight of how many grams?
A shopkeeper sells sugar at ₹30 per kg, which he has bought at ₹24 per kg. Being dishonest, he also gives only y gm of sugar instead of 1000 gm that is mentioned on the weight. In this way, the shopkeeper manages to make an overall profit of 66 2/3%. What is the value of y?
A trader lost 20% by selling a watch for ₹1024. What percentage will he gain by selling it for ₹1472?
A dishonest shopkeeper pretends to sell his goods at cost price. However, he uses a false weight on which 984 gm is written, but actually weighs lesser. Using this false weight, the shopkeeper makes a gain of 23%. The actual measure of the weight used is:
A retailer would have made a profit of 18% if he had sold an article at its marked price. If the marked price of the article is ₹826, then the cost price of the article is:
A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for ₹10.50 less, he would have gained 30%. Find the cost price of the article.
A dealer allows a 30% discount on the marked price of an item. What is the marked price of the item if its sale price is ₹12460?
A shopkeeper bought an article for ₹319.60. Approximately, at what price should he sell the article to make a 25% profit?
An article is marked at 50% above its cost price. If the marked price of the article is ₹1,500, then the cost price of the article is:
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?
