The percent profit earned by selling an article at Rs. 6720 is equal to the percent loss incurred on selling the same article at Rs. 4480. What will be the percent profit of the ar... The percent profit earned by selling an article at Rs. 6720 is equal to the percent loss incurred on selling the same article at Rs. 4480. What will be the percent profit of the article, if it is sold at Rs. 6440?
Understand the Problem
The question is asking to determine the percent profit from selling an article at Rs. 6440, given the information about its selling price at Rs. 6720 (profit) and Rs. 4480 (loss). We will solve it by first finding the cost price from the given profit and loss percentages.
Answer
The percent profit earned by selling the article at Rs. 6440 is \(15\%\).
Answer for screen readers
The percent profit when sold at Rs. 6440 is (15%).
Steps to Solve
- Determine the Cost Price (CP)
To find the cost price, we first need to define the selling price (SP) at profit and loss.
Let the cost price be $CP$.
Profit selling price is given as: $$ SP_{profit} = CP + Profit = 6720 $$
Loss selling price is given as: $$ SP_{loss} = CP - Loss = 4480 $$
- Set Up the Equations
From the first equation for profit: $$ CP + Profit = 6720 $$ From the second equation for loss: $$ CP - Loss = 4480 $$
- Relate Profit and Loss
Let the profit percentage be $P%$, and the loss percentage be $L%$. Since the problem states that the percent profit is equal to the percent loss, we can say: $$ \frac{Profit}{CP} \times 100 = \frac{Loss}{CP} \times 100 \implies Profit = Loss $$
- Express Loss in terms of CP
Now substituting the expressions for profit and loss in terms of CP: $$ Profit = CP + (6720 - CP) = 6720 - CP $$ $$ Loss = CP - (4480 - CP) = CP - 4480 $$
Since profit equals loss: $$ 6720 - CP = CP - 4480 $$
- Solve for CP
Combine like terms: $$ 6720 + 4480 = 2CP $$ $$ 11200 = 2CP $$ Dividing both sides by 2 gives: $$ CP = 5600 $$
- Determine Profit (when SP is Rs. 6440)
To find the percentage profit when sold at Rs. 6440, we use: $$ Profit = SP - CP = 6440 - 5600 = 840 $$
- Calculate Percent Profit
Now calculate the percent profit: $$ Percent\ Profit = \left( \frac{Profit}{CP} \times 100 \right) = \left( \frac{840}{5600} \times 100 \right) = 15% $$
The percent profit when sold at Rs. 6440 is (15%).
More Information
In this problem, we find the cost price of an article based on given selling prices at profit and loss, and then use that to compute the percent profit when the article is sold at a different price.
Tips
Common mistakes include:
- Misunderstanding that profit equals loss; the problem states that their percentages are equal, not the amounts.
- Confusing selling price with cost price; proper identification of these terms is essential to find the correct percentage profit.
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