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
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?
