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Instead of a metre scale, a cloth merchant uses a faulty 120 cm scale while buying, but uses a faulty 80 cm scale while selling the same cloth. If he offers a discount of 20%, what is his overall profit percentage?
- a)20%
- b)25%
- c)40%
- d)15%
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Instead of a metre scale, a cloth merchant uses a faulty 120 cm scale ...
Let's say the cost of the cloth is x rs per metre. Because of the faulty meter, he is paying x for 120 cms when buying.
So cost of 100 cms = 100x/120.
He is selling 80 cms for x, so selling price of 100cms of cloth is 100x/80.
discount = 20%
so the effective selling price is 8 * 100x/80 = x
profit = SP - CP = x - 100x/120 = x/6
Profit % = x/6 divided by 100x/120 = 20%
So cost of 100 cms = 100x/120.
He is selling 80 cms for x, so selling price of 100cms of cloth is 100x/80.
discount = 20%
so the effective selling price is 8 * 100x/80 = x
profit = SP - CP = x - 100x/120 = x/6
Profit % = x/6 divided by 100x/120 = 20%
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Community Answer
Instead of a metre scale, a cloth merchant uses a faulty 120 cm scale ...
Understanding the Faulty Scale Usage
The cloth merchant uses two faulty scales:
- Buying Scale: 120 cm (instead of 100 cm)
- Selling Scale: 80 cm (instead of 100 cm)
Calculating Effective Lengths
- When buying 120 cm, he is actually getting 120 cm of cloth but pays for only 100 cm.
- When selling 80 cm, he is giving away 80 cm of cloth but charges for 100 cm.
Calculating Cost Price and Selling Price
- Cost Price (CP): Assume he buys cloth worth 100 units (for 100 cm).
- Effective Length Bought: 120 cm for 100 units, so the cost per cm is 100/120 = 5/6 units.
- Selling Price (SP): He sells 80 cm but charges for 100 cm.
- Selling Price with Discount: Selling price is 100 units, but with a 20% discount, he sells for 100 - 20% of 100 = 80 units.
Calculating Profit Percentage
- Total Effective Length Sold: 80 cm.
- Effective Cost of 80 cm: Cost for 80 cm is 80 * (5/6) = 400/6 = 66.67 units.
- Profit Calculation: Profit = SP - CP = 80 - 66.67 = 13.33 units.
Profit Percentage Calculation
- Profit Percentage = (Profit/CP) * 100 = (13.33/66.67) * 100 = 20%.
Conclusion
The overall profit percentage of the cloth merchant, after considering the faulty scales and the discount offered, is 20%. Thus, the correct answer is option A.
The cloth merchant uses two faulty scales:
- Buying Scale: 120 cm (instead of 100 cm)
- Selling Scale: 80 cm (instead of 100 cm)
Calculating Effective Lengths
- When buying 120 cm, he is actually getting 120 cm of cloth but pays for only 100 cm.
- When selling 80 cm, he is giving away 80 cm of cloth but charges for 100 cm.
Calculating Cost Price and Selling Price
- Cost Price (CP): Assume he buys cloth worth 100 units (for 100 cm).
- Effective Length Bought: 120 cm for 100 units, so the cost per cm is 100/120 = 5/6 units.
- Selling Price (SP): He sells 80 cm but charges for 100 cm.
- Selling Price with Discount: Selling price is 100 units, but with a 20% discount, he sells for 100 - 20% of 100 = 80 units.
Calculating Profit Percentage
- Total Effective Length Sold: 80 cm.
- Effective Cost of 80 cm: Cost for 80 cm is 80 * (5/6) = 400/6 = 66.67 units.
- Profit Calculation: Profit = SP - CP = 80 - 66.67 = 13.33 units.
Profit Percentage Calculation
- Profit Percentage = (Profit/CP) * 100 = (13.33/66.67) * 100 = 20%.
Conclusion
The overall profit percentage of the cloth merchant, after considering the faulty scales and the discount offered, is 20%. Thus, the correct answer is option A.
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Instead of a metre scale, a cloth merchant uses a faulty 120 cm scale while buying, but uses a faulty 80 cm scale while selling the same cloth. If he offers a discount of 20%, what is his overall profit percentage?a)20%b)25%c)40%d)15%Correct answer is option 'A'. Can you explain this answer?
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