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If the selling price of an article is doubled, then its loss percentage gets converted into the equal profit percentage. What is the loss percentage?
- a)16.66
- b)50
- c)33.33
- d)37.5
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If the selling price of an article is doubled, then its loss percentag...
Loss % = {(Cost price – selling price)/cost price} × 100
Profit % = {(2 × selling price – cost price)/cost price} × 100
According to question,
{(Cost price – selling price)/cost price} × 100 = {(2 × selling price – cost price)/cost price} × 100
⇒ cost price – selling price = 2 × selling price – cost price
⇒ 2 × cost price = 3 × selling price
⇒ Selling price/cost price = 2/3
Now,
∴ Loss % = {(Cost price – selling price)/cost price} × 100 = {1 – (selling price/cost price)} × 100 = {1 – (2/3)} × 100 = 33.33%
Profit % = {(2 × selling price – cost price)/cost price} × 100
According to question,
{(Cost price – selling price)/cost price} × 100 = {(2 × selling price – cost price)/cost price} × 100
⇒ cost price – selling price = 2 × selling price – cost price
⇒ 2 × cost price = 3 × selling price
⇒ Selling price/cost price = 2/3
Now,
∴ Loss % = {(Cost price – selling price)/cost price} × 100 = {1 – (selling price/cost price)} × 100 = {1 – (2/3)} × 100 = 33.33%
Most Upvoted Answer
If the selling price of an article is doubled, then its loss percentag...
Understanding the Problem
The problem states that when the selling price of an article is doubled, the loss percentage transforms into an equivalent profit percentage. We need to find the loss percentage.
Let’s Define Key Terms
- Cost Price (CP): The original price paid for the article.
- Selling Price (SP): The price at which the article is sold.
- Loss Percentage: The percentage of the loss calculated based on the cost price.
Formulas to Remember
- Loss = CP - SP
- Loss Percentage = (Loss / CP) x 100
- Profit = SP - CP
- Profit Percentage = (Profit / CP) x 100
Setting Up the Equation
1. Let the original selling price (SP) be S.
2. If there is a loss, then SP = CP - Loss.
3. When SP is doubled, SP becomes 2S.
Now, at this new selling price, we have a profit:
- New Selling Price (2S) = CP + Profit
Equating Loss Percentage and Profit Percentage
Since loss percentage equals profit percentage:
- Loss Percentage = (CP - S) / CP * 100
- Profit Percentage = (2S - CP) / CP * 100
Setting these equal to each other gives:
(CP - S) / CP = (2S - CP) / CP
Solving for Loss Percentage
1. Cross-multiplying leads to:
CP - S = 2S - CP
2. Rearranging yields:
2CP = 3S
3. Thus, S = (2/3)CP
Now substituting back to find the loss percentage:
- Loss = CP - SP = CP - (2/3)CP = (1/3)CP
- Loss Percentage = ((1/3)CP / CP) x 100 = 33.33%
Conclusion
The loss percentage is 33.33%, confirming that option 'C' is correct.
The problem states that when the selling price of an article is doubled, the loss percentage transforms into an equivalent profit percentage. We need to find the loss percentage.
Let’s Define Key Terms
- Cost Price (CP): The original price paid for the article.
- Selling Price (SP): The price at which the article is sold.
- Loss Percentage: The percentage of the loss calculated based on the cost price.
Formulas to Remember
- Loss = CP - SP
- Loss Percentage = (Loss / CP) x 100
- Profit = SP - CP
- Profit Percentage = (Profit / CP) x 100
Setting Up the Equation
1. Let the original selling price (SP) be S.
2. If there is a loss, then SP = CP - Loss.
3. When SP is doubled, SP becomes 2S.
Now, at this new selling price, we have a profit:
- New Selling Price (2S) = CP + Profit
Equating Loss Percentage and Profit Percentage
Since loss percentage equals profit percentage:
- Loss Percentage = (CP - S) / CP * 100
- Profit Percentage = (2S - CP) / CP * 100
Setting these equal to each other gives:
(CP - S) / CP = (2S - CP) / CP
Solving for Loss Percentage
1. Cross-multiplying leads to:
CP - S = 2S - CP
2. Rearranging yields:
2CP = 3S
3. Thus, S = (2/3)CP
Now substituting back to find the loss percentage:
- Loss = CP - SP = CP - (2/3)CP = (1/3)CP
- Loss Percentage = ((1/3)CP / CP) x 100 = 33.33%
Conclusion
The loss percentage is 33.33%, confirming that option 'C' is correct.
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If the selling price of an article is doubled, then its loss percentage gets converted into the equal profit percentage. What is the loss percentage?a)16.66b)50c)33.33d)37.5Correct answer is option 'C'. Can you explain this answer?
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