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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%
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If the selling price of an article is doubled, then its loss percentag...
Problem:
The selling price of an article is doubled, and as a result, the loss percentage gets converted into an equal profit percentage. We need to find the loss percentage.
Solution:
Let's assume the cost price (CP) of the article is 'C' and the loss percentage is 'L'. Therefore, the selling price (SP) can be calculated using the formula:
SP = CP - (L/100) * CP
When the selling price is doubled, it becomes 2SP. So, the new selling price can be expressed as:
2SP = 2 * [CP - (L/100) * CP]
2SP = 2CP - (2L/100) * CP
2SP = CP - (L/50) * CP
Profit Percentage:
When the selling price is doubled, the profit percentage can be calculated using the formula:
Profit Percentage = [(Selling Price - Cost Price) / Cost Price] * 100
In this case, the profit percentage is equal to the loss percentage (L). So, we have:
L = [(2SP - CP) / CP] * 100
L = [(CP - (L/50) * CP - CP) / CP] * 100
L = [(-L/50) * CP / CP] * 100
L = (-L/50) * 100
L = -2L
Solving for L:
To find the value of L, we solve the equation:
L = -2L
Adding 2L to both sides:
3L = 0
Dividing both sides by 3:
L = 0
Therefore, the loss percentage is 0%.
Conclusion:
The loss percentage is 0%.
The selling price of an article is doubled, and as a result, the loss percentage gets converted into an equal profit percentage. We need to find the loss percentage.
Solution:
Let's assume the cost price (CP) of the article is 'C' and the loss percentage is 'L'. Therefore, the selling price (SP) can be calculated using the formula:
SP = CP - (L/100) * CP
When the selling price is doubled, it becomes 2SP. So, the new selling price can be expressed as:
2SP = 2 * [CP - (L/100) * CP]
2SP = 2CP - (2L/100) * CP
2SP = CP - (L/50) * CP
Profit Percentage:
When the selling price is doubled, the profit percentage can be calculated using the formula:
Profit Percentage = [(Selling Price - Cost Price) / Cost Price] * 100
In this case, the profit percentage is equal to the loss percentage (L). So, we have:
L = [(2SP - CP) / CP] * 100
L = [(CP - (L/50) * CP - CP) / CP] * 100
L = [(-L/50) * CP / CP] * 100
L = (-L/50) * 100
L = -2L
Solving for L:
To find the value of L, we solve the equation:
L = -2L
Adding 2L to both sides:
3L = 0
Dividing both sides by 3:
L = 0
Therefore, the loss percentage is 0%.
Conclusion:
The loss percentage is 0%.
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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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