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If 80% of total articles are sold at a loss of 15% and remaining articles are sold at a profit of 15%, then what will be the overall loss percentage?
- a)15
- b)6
- c)9
- d)12
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If 80% of total articles are sold at a loss of 15% and remaining artic...
Let the cost price of all articles be Rs. ‘x’
Cost price of 80% articles = 80% of x = (4/5)x
But, there is a loss of 15% = 15% of (4/5)x = 3/20 × (4/5)x = (3/25)x
⇒ Selling price of 80% articles = (4/5)x - (3/25)x = (17/25)x
Similarly,
Cost price of remaining articles = x - (4/5)x = x/5
But, there is a profit of 15% = 15% of x/5 = 3/20 × x/5 = (3/100)x
⇒ Selling price of remaining articles = x/5 + (3/100)x = (23/100)x
Hence,
Selling price of all articles = (17/25)x + (23/100)x = (91/100)x
⇒ Overall loss = x - (91/100)x = (9/100)x
∴ Overall loss percentage = (9x/100)/x × 100 = 9%
Cost price of 80% articles = 80% of x = (4/5)x
But, there is a loss of 15% = 15% of (4/5)x = 3/20 × (4/5)x = (3/25)x
⇒ Selling price of 80% articles = (4/5)x - (3/25)x = (17/25)x
Similarly,
Cost price of remaining articles = x - (4/5)x = x/5
But, there is a profit of 15% = 15% of x/5 = 3/20 × x/5 = (3/100)x
⇒ Selling price of remaining articles = x/5 + (3/100)x = (23/100)x
Hence,
Selling price of all articles = (17/25)x + (23/100)x = (91/100)x
⇒ Overall loss = x - (91/100)x = (9/100)x
∴ Overall loss percentage = (9x/100)/x × 100 = 9%
Most Upvoted Answer
If 80% of total articles are sold at a loss of 15% and remaining artic...
Calculation of Overall Loss Percentage:
- Let's assume the total number of articles to be 100 for easier calculations.
- 80% of 100 articles are sold at a loss of 15%, which means 80 articles are sold at a loss.
- The remaining 20 articles are sold at a profit of 15%.
Calculating the Loss:
- For the 80 articles sold at a loss of 15%, the loss percentage is 15%.
- Therefore, the overall loss for these articles would be 80 * 15% = 1200%
- For the 20 articles sold at a profit of 15%, the profit percentage is 15%.
- Therefore, the overall profit for these articles would be 20 * 15% = 300%
Calculating the Overall Loss Percentage:
- To find the overall loss percentage, we need to consider the net loss.
- Net loss = Loss - Profit = 1200% - 300% = 900%
- Since the net loss is calculated on the total number of articles (100), the overall loss percentage would be 900% / 100 = 9%
Therefore, the overall loss percentage in this scenario is 9%.
This calculation helps in understanding the impact of selling articles at different profit and loss percentages on the overall outcome.
- Let's assume the total number of articles to be 100 for easier calculations.
- 80% of 100 articles are sold at a loss of 15%, which means 80 articles are sold at a loss.
- The remaining 20 articles are sold at a profit of 15%.
Calculating the Loss:
- For the 80 articles sold at a loss of 15%, the loss percentage is 15%.
- Therefore, the overall loss for these articles would be 80 * 15% = 1200%
- For the 20 articles sold at a profit of 15%, the profit percentage is 15%.
- Therefore, the overall profit for these articles would be 20 * 15% = 300%
Calculating the Overall Loss Percentage:
- To find the overall loss percentage, we need to consider the net loss.
- Net loss = Loss - Profit = 1200% - 300% = 900%
- Since the net loss is calculated on the total number of articles (100), the overall loss percentage would be 900% / 100 = 9%
Therefore, the overall loss percentage in this scenario is 9%.
This calculation helps in understanding the impact of selling articles at different profit and loss percentages on the overall outcome.
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