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A dishonest shopkeeper takes 20% more than the indicated weight when he purchases the items from the dealer. He gives 20% less than the indicated weight to his customer at the cost price, then find the profit percentage of the shopkeeper.
- a)44.44%
- b)66.66%
- c)50%
- d)37.75%
- e)33.33%
Correct answer is option 'C'. Can you explain this answer?
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To find the profit percentage of the shopkeeper, we need to understand the process of how the shopkeeper manipulates the weights and calculate the final selling price.
Let's assume the indicated weight of an item is 100 grams and the cost price is $1 per gram.
1. Purchasing from the dealer:
The dishonest shopkeeper takes 20% more than the indicated weight when purchasing the items from the dealer. So, the shopkeeper will actually get 120 grams for the price of 100 grams.
2. Selling to the customer:
The shopkeeper gives 20% less than the indicated weight to the customer at the cost price. So, the customer will receive only 80 grams instead of 100 grams.
3. Calculating the selling price:
Since the cost price is $1 per gram, the cost price for 80 grams will be $80. However, the shopkeeper wants to make a profit, so he will increase the selling price.
Let's say the selling price per gram is $x. Therefore, the selling price for 80 grams will be 80x.
4. Calculating the profit percentage:
To find the profit percentage, we need to compare the profit with the cost price and express it as a percentage.
Profit = Selling Price - Cost Price
Profit = 80x - $80
Profit Percentage = (Profit / Cost Price) * 100
Profit Percentage = ((80x - $80) / $80) * 100
Now, we need to solve the equation to find the value of x and further calculate the profit percentage.
(80x - $80) / $80 = 50% (Given in option C)
(80x - $80) / $80 = 0.50
80x - $80 = 0.50 * $80
80x - $80 = $40
80x = $120
x = $120 / 80
x = $1.50
Profit Percentage = ((80 * $1.50 - $80) / $80) * 100
Profit Percentage = (120 - 80) / 80 * 100
Profit Percentage = 40 / 80 * 100
Profit Percentage = 0.50 * 100
Profit Percentage = 50%
Therefore, the profit percentage of the shopkeeper is 50%, which is option C.
Let's assume the indicated weight of an item is 100 grams and the cost price is $1 per gram.
1. Purchasing from the dealer:
The dishonest shopkeeper takes 20% more than the indicated weight when purchasing the items from the dealer. So, the shopkeeper will actually get 120 grams for the price of 100 grams.
2. Selling to the customer:
The shopkeeper gives 20% less than the indicated weight to the customer at the cost price. So, the customer will receive only 80 grams instead of 100 grams.
3. Calculating the selling price:
Since the cost price is $1 per gram, the cost price for 80 grams will be $80. However, the shopkeeper wants to make a profit, so he will increase the selling price.
Let's say the selling price per gram is $x. Therefore, the selling price for 80 grams will be 80x.
4. Calculating the profit percentage:
To find the profit percentage, we need to compare the profit with the cost price and express it as a percentage.
Profit = Selling Price - Cost Price
Profit = 80x - $80
Profit Percentage = (Profit / Cost Price) * 100
Profit Percentage = ((80x - $80) / $80) * 100
Now, we need to solve the equation to find the value of x and further calculate the profit percentage.
(80x - $80) / $80 = 50% (Given in option C)
(80x - $80) / $80 = 0.50
80x - $80 = 0.50 * $80
80x - $80 = $40
80x = $120
x = $120 / 80
x = $1.50
Profit Percentage = ((80 * $1.50 - $80) / $80) * 100
Profit Percentage = (120 - 80) / 80 * 100
Profit Percentage = 40 / 80 * 100
Profit Percentage = 0.50 * 100
Profit Percentage = 50%
Therefore, the profit percentage of the shopkeeper is 50%, which is option C.
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