Note: round off to two decimal places
Understanding Anita's Gain Percentage
Anita sold a quantity of school bags and wants to determine her profit margin. Specifically, she sold 2800 school bags. The problem states that the profit Anita earned is equivalent to the sale price of 420 school bags. The goal is to calculate the gain percentage she achieved on this sale.
Defining Key Concepts in Profit Calculation
To solve this problem, let's clarify the terms:
- Selling Price (SP): The price at which an item is sold.
- Cost Price (CP): The original price paid for an item.
- Profit: The amount earned when the SP is greater than the CP. It is calculated as Profit = SP - CP.
- Gain Percentage: The profit expressed as a percentage of the cost price. The formula is: $$ \text{Gain Percentage} = \frac{\text{Profit}}{\text{Cost Price}} \times 100 $$
Setting Up the Calculation for School Bags
Let's assume:
- The selling price of one school bag is $S$.
- The cost price of one school bag is $C$.
Based on the information given:
- Total Selling Price for 2800 school bags = $2800 \times S$
- Profit earned = Selling price of 420 school bags = $420 \times S$
We know that Profit = Total Selling Price - Total Cost Price. We can use this to find the Total Cost Price (CP) for the 2800 school bags:
Total CP = Total SP - Profit
Total CP = $2800S - 420S$
Total CP = $2380S$
Calculating Anita's Gain Percentage
Now we can use the formula for Gain Percentage:
$$ \text{Gain Percentage} = \frac{\text{Profit}}{\text{Total Cost Price}} \times 100 $$Substitute the values we found:
$$ \text{Gain Percentage} = \frac{420S}{2380S} \times 100 $$The $S$ variable cancels out, simplifying the calculation:
$$ \text{Gain Percentage} = \frac{420}{2380} \times 100 $$Let's simplify the fraction $\frac{420}{2380}$:
Divide both numerator and denominator by 10: $\frac{42}{238}$
Divide both by 14: $\frac{42 \div 14}{238 \div 14} = \frac{3}{17}$
So, the calculation becomes:
$$ \text{Gain Percentage} = \frac{3}{17} \times 100 $$ $$ \text{Gain Percentage} = \frac{300}{17} $$Final Result and Rounding
To find the percentage, we divide 300 by 17:
$$ \frac{300}{17} \approx 17.64705... $$
The question asks to round the answer to two decimal places. Rounding $17.64705...$ gives:
$$ 17.65\% $$
Therefore, Anita earned a gain percentage of 17.65% on the sale of the school bags.
Similar Questions
- P sells a Laptop to Q at a loss of 25% and Q sells the laptop to R at a profit of 20%. If R purchased the laptop for 22,500, then what was the cost (in ₹) of the laptop for P?
- The selling price of y items is equal to the cost price of 540 items. If the profit made is 44%, then find the value of y.
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 _______.
- The profit earned after selling an article for ₹6,250 is the same as the loss incurred after selling the article for ₹3,750. Find the cost price of the article.
Shyam bought a chair for ₹1,563 and spent ₹350 on its repairing. He sold it for ₹2,398. Find his profit percentage (correct to two places of decimals).
- A chair is bought for ₹600 and sold for ₹750. Find the profit percentage.
- The difference between the cost price and the selling price of a table lamp is ₹540. If the profit is 30%, then the selling price (in) is:
- If the market price of a bedsheet is 24% above the cost price and a discount of 15% is declared on it, then find the gain percentage.
- Ram buys 13 balls for Rs.390 and sells them at the rate of Rs.33 per ball. Find his gain percentage.
- If the selling price of 10 chairs is the same as the cost price of 8 chairs, find the loss percentage.
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?
