Cost Price: Initial 40% Profit
This problem involves finding the original cost price (CP) of an article by setting up equations based on profit percentages and changes in cost and selling prices.
Article Conditions: Increased Cost, Reduced SP
Let the original cost price (CP) of the article be denoted by \(x\).
The initial profit is 40%. Therefore, the original Selling Price (SP) is:
Original SP = \(x + (0.40 \times x) = 1.40x\)
Two conditions are applied:
- The cost price increases by ₹28. New CP = \(x + 28\).
- The selling price decreases by ₹84. New SP = \(1.40x - 84\).
After these adjustments, the profit becomes 37.5%.
Profit Percentage Equation Setup
The profit percentage is calculated as \(\frac{SP - CP}{CP} \times 100\). Using the new values:
\(37.5 = \frac{(1.40x - 84) - (x + 28)}{x + 28} \times 100\)
Convert the percentage to a decimal:
\(0.375 = \frac{1.40x - 84 - x - 28}{x + 28}\)
Simplify the numerator:
\(0.375 = \frac{0.40x - 112}{x + 28}\)
Solve for Original Cost Price Variable
To solve for \(x\), we rearrange the equation:
Cross-multiply:
\(0.375(x + 28) = 0.40x - 112\)
Distribute:
\(0.375x + (0.375 \times 28) = 0.40x - 112\)
\(0.375x + 10.5 = 0.40x - 112\)
Group terms:
\(112 + 10.5 = 0.40x - 0.375x\)
\(122.5 = 0.025x\)
Isolate \(x\):
\(x = \frac{122.5}{0.025}\)
\(x = 4900\)
Result: Original Cost Price Determined
The original cost price of the article is ₹4,900.
Similar Questions
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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?
