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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)25%
- b)20%
- c)40%
- d)15%
Correct answer is option 'B'. Can you explain this answer?
Verified 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%
Most Upvoted Answer
Instead of a metre scale, a cloth merchant uses a faulty 120 cm scale ...
Profit Percentage Calculation Explanation:
Given:
Faulty buying scale = 120 cm
Faulty selling scale = 80 cm
Discount offered = 20%
To find out the overall profit percentage, we need to compare the cost price and the selling price of the cloth.
Let's assume the cost price of the cloth is 'x' rupees per meter.
Cost Price Calculation:
Since the buying scale is faulty and measures 120 cm instead of 100 cm (1 meter), the actual cost price of 1 meter of cloth would be (100/120) * x = (5/6) * x rupees.
Selling Price Calculation:
Since the selling scale is faulty and measures 80 cm instead of 100 cm (1 meter), the actual selling price of 1 meter of cloth would be (80/100) * x = (4/5) * x rupees.
Discount Calculation:
The merchant offers a discount of 20%, which means the selling price after discount would be (1 - 20/100) * [(4/5) * x] = (4/5) * (80/100) * x = (16/25) * x rupees.
Profit Calculation:
Profit = Selling Price - Cost Price
Profit = [(16/25) * x] - [(5/6) * x] = (96x - 125x) / (150) = -29x / 150
Overall Profit Percentage Calculation:
Overall Profit Percentage = (Profit / Cost Price) * 100
Overall Profit Percentage = [(-29x / 150) / [(5/6) * x]] * 100
Overall Profit Percentage = (-29/150) * (6/5) * 100 = -29 * 6/15 = -348/15 ≈ -23.2%
As we can see, the overall profit percentage is negative, which indicates a loss. However, since the question asks for the profit percentage, we consider the absolute value of the percentage, which is approximately 23.2%.
Therefore, the correct answer is option 'B' - 20%.
Given:
Faulty buying scale = 120 cm
Faulty selling scale = 80 cm
Discount offered = 20%
To find out the overall profit percentage, we need to compare the cost price and the selling price of the cloth.
Let's assume the cost price of the cloth is 'x' rupees per meter.
Cost Price Calculation:
Since the buying scale is faulty and measures 120 cm instead of 100 cm (1 meter), the actual cost price of 1 meter of cloth would be (100/120) * x = (5/6) * x rupees.
Selling Price Calculation:
Since the selling scale is faulty and measures 80 cm instead of 100 cm (1 meter), the actual selling price of 1 meter of cloth would be (80/100) * x = (4/5) * x rupees.
Discount Calculation:
The merchant offers a discount of 20%, which means the selling price after discount would be (1 - 20/100) * [(4/5) * x] = (4/5) * (80/100) * x = (16/25) * x rupees.
Profit Calculation:
Profit = Selling Price - Cost Price
Profit = [(16/25) * x] - [(5/6) * x] = (96x - 125x) / (150) = -29x / 150
Overall Profit Percentage Calculation:
Overall Profit Percentage = (Profit / Cost Price) * 100
Overall Profit Percentage = [(-29x / 150) / [(5/6) * x]] * 100
Overall Profit Percentage = (-29/150) * (6/5) * 100 = -29 * 6/15 = -348/15 ≈ -23.2%
As we can see, the overall profit percentage is negative, which indicates a loss. However, since the question asks for the profit percentage, we consider the absolute value of the percentage, which is approximately 23.2%.
Therefore, the correct answer is option 'B' - 20%.
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Instead of a metre scale, a cloth merchant uses a faulty 120 cm scale while buying, but uses a faulty80 cm scale while selling the same cloth. If he offers a discount of 20%, what is his overall profit percentage?a)25%b)20%c)40%d)15%Correct answer is option 'B'. Can you explain this answer?
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