Understanding the Vendor's Profit Calculation
This problem involves calculating the number of items (pens) a vendor needs to buy and sell to achieve a specific profit target. We are given the purchase details (cost price) and selling details (selling price) in batches, and the desired total profit.
Calculating Cost Price (CP) and Selling Price (SP) per Pen
First, let's determine the cost price and selling price for a single pen.
- Cost Price Calculation: The vendor buys 20 pens for ₹15.
To find the cost price of one pen, we divide the total cost by the number of pens:
CP per pen = ₹15 / 20
CP per pen = ₹$ \frac{15}{20} = ₹ \frac{3}{4} $ or ₹0.75
- Selling Price Calculation: The vendor sells 15 pens for ₹20.
To find the selling price of one pen, we divide the total selling amount by the number of pens sold:
SP per pen = ₹20 / 15
SP per pen = ₹$ \frac{20}{15} = ₹ \frac{4}{3} $
Determining Profit per Pen
Profit is the difference between the selling price and the cost price. Let's calculate the profit earned on each pen sold.
Profit per pen = SP per pen - CP per pen
Profit per pen = ₹$ \frac{4}{3} - ₹ \frac{3}{4} $
To subtract these fractions, we find a common denominator, which is 12:
Profit per pen = ₹$ \left( \frac{4 \times 4}{3 \times 4} \right) - \left( \frac{3 \times 3}{4 \times 3} \right) $
Profit per pen = ₹$ \frac{16}{12} - \frac{9}{12} $
Profit per pen = ₹$ \frac{16 - 9}{12} = ₹ \frac{7}{12} $
So, the vendor earns a profit of ₹$ \frac{7}{12} $ on each pen.
Calculating the Number of Pens for Target Profit
The vendor wants to earn a total profit of ₹245. We know the profit made per pen. To find the total number of pens needed, we divide the total desired profit by the profit per pen.
Number of pens = Total Desired Profit / Profit per pen
Number of pens = ₹245 / ₹$ \frac{7}{12} $
To divide by a fraction, we multiply by its reciprocal:
Number of pens = $ 245 \times \frac{12}{7} $
First, divide 245 by 7:
$ \frac{245}{7} = 35 $
Now, multiply the result by 12:
Number of pens = $ 35 \times 12 $
Number of pens = 420
Conclusion
Therefore, the vendor needs to buy and sell 420 pens to earn a profit of ₹245.
Similar Questions
The selling price of 84 items is equal to the cost price of 105 items. What is the percentage of profit gained in the transaction?
Two articles were sold for Rs.3,000 each, with no loss and profit in the entire transaction. If one was sold at a profit of 25%, then the loss incurred on the second article is _______.
- A man sells a cow for Rs.22,000 and gains 10%. At what price should he sell the same cow, in order to gain 14%?
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?
