A shopkeeper marks the price of an article at ₹5,180. Find the cost price if after allowing a discount of 31% he still gains 5% on the cost price.
₹3,404
This question asks us to find the cost price (CP) of an article when we know its marked price (MP), the discount offered, and the subsequent gain (profit) made by the shopkeeper.
Calculating Selling Price After Discount
First, the shopkeeper marks the article at ₹5,180. They offer a discount of 31%. The selling price (SP) is the marked price minus the discount amount.
The formula to calculate the selling price after a discount is:
$$ \text{SP} = \text{MP} \times (1 - \text{Discount Rate}) $$Given:
- Marked Price (MP) = ₹5,180
- Discount Rate = 31% = 0.31
Plugging the values into the formula:
$$ \text{SP} = 5180 \times (1 - 0.31) $$ $$ \text{SP} = 5180 \times 0.69 $$ $$ \text{SP} = 3574.2 $$So, the selling price of the article is ₹3,574.20.
Calculating Cost Price with Profit
The shopkeeper still gains 5% on the cost price after offering the discount. This means the selling price we just calculated includes a 5% profit over the original cost price.
The relationship between Selling Price (SP), Cost Price (CP), and Profit Percentage is:
$$ \text{SP} = \text{CP} \times (1 + \text{Profit Rate}) $$Given:
- Selling Price (SP) = ₹3,574.20
- Profit Rate = 5% = 0.05
We need to find the Cost Price (CP). Rearranging the formula to solve for CP:
$$ \text{CP} = \frac{\text{SP}}{(1 + \text{Profit Rate})} $$Plugging in the values:
$$ \text{CP} = \frac{3574.20}{(1 + 0.05)} $$ $$ \text{CP} = \frac{3574.20}{1.05} $$ $$ \text{CP} = 3404 $$Therefore, the cost price of the article is ₹3,404.
Final Answer Summary
The calculation shows that the cost price required to achieve a 5% profit after a 31% discount on a marked price of ₹5,180 is ₹3,404.
Summary Table:
| Marked Price (MP) | ₹5,180 |
| Discount Rate | 31% |
| Selling Price (SP) | ₹3,574.20 |
| Profit Rate | 5% |
| Cost Price (CP) | ₹3,404 |
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?
