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
By selling an article for Rs. 2,200, a profit of 10% is earned. If the same article is sold for Rs. 2,600, then what will be the gain percentage?
By selling an article for Rs. 640, a person loses 15% of its selling price. At what price (in Rs.) should he sell it to gain 15% on its cost price?
The selling prices of articles A and B are the same. A is sold at a profit of 28 percent and B is sold at a loss of 24 percent. If the total selling price of the both articles is Rs. 48640, then what is the cost price of A and B, respectively ?
The cost price of an article is Rs. 2800. Profit as a percentage of selling price is 20 percent. What is the actual profit (in Rs.) ?
A trader bought 640 kg of rice. He sold a part of rice at 20% profit and the rest at 5% loss. He earned a profit of 15% in the entire transaction. What is the quantity (in kg) of rice that he sold at 5% loss?
