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A dishonest seller professes to sell his milk at cost price but he mixes water with milk and gains 25 percent, then find the percentage of milk in the mixture.
- a)60%
- b)70%
- c)80%
- d)90%
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A dishonest seller professes to sell his milk at cost price but he mix...
Answer – c) 80% Explanation : Suppose initially there is 100ltr of milk costing 100 rupees.
Now he gains 25% means in 100ltr of milk he add 25ltr water, so percentage of milk in the mixture = (100/125)*100 = 80%
Now he gains 25% means in 100ltr of milk he add 25ltr water, so percentage of milk in the mixture = (100/125)*100 = 80%
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A dishonest seller professes to sell his milk at cost price but he mix...
To solve this problem, we need to first understand the concept of cost price and the percentage gain.
Cost Price:
The cost price of a product is the price at which it is bought or produced. In this case, the dishonest seller claims to sell the milk at cost price, which means he is selling it without any profit.
Percentage Gain:
The percentage gain is the profit percentage earned on the cost price. In this case, the dishonest seller is gaining 25% by mixing water with milk.
Now, let's solve the problem step by step:
Step 1: Assume the cost price of 1 liter of milk is 100 units. Since the seller claims to sell the milk at cost price, he is selling 1 liter of milk for 100 units.
Step 2: The dishonest seller mixes water to increase his profit. Let's assume he adds 'x' liters of water to 1 liter of milk. So, the total quantity of the mixture will be 1 + x liters.
Step 3: The dishonest seller gains 25% by mixing water with milk. This means that the selling price of the mixture is 125% of the cost price.
So, the selling price of the mixture is (125/100) * (100 + x) units.
Step 4: As the seller claims to sell the milk at cost price, the selling price should be equal to the cost price.
Therefore, we can write the equation as: (125/100) * (100 + x) = 100.
Step 5: Simplifying the equation, we have: (5/4) * (100 + x) = 100.
Step 6: Cross-multiplying, we get: 5(100 + x) = 4 * 100.
Step 7: Expanding the equation, we have: 500 + 5x = 400.
Step 8: Solving for 'x', we get: 5x = 400 - 500 = -100.
Step 9: Dividing both sides of the equation by 5, we get: x = -100/5 = -20.
Step 10: Since we cannot have a negative quantity of water, this result is not valid. Therefore, our assumption that the cost price is 100 units is incorrect.
Step 11: Let's try a different assumption for the cost price. Let's assume the cost price of 1 liter of milk is 'y' units.
Step 12: Following the same steps as above, we can write the equation as: (125/100) * (y + x) = y.
Step 13: Simplifying the equation, we have: (5/4) * (y + x) = y.
Step 14: Cross-multiplying, we get: 5(y + x) = 4y.
Step 15: Expanding the equation, we have: 5y + 5x = 4y.
Step 16: Simplifying the equation, we get:
Cost Price:
The cost price of a product is the price at which it is bought or produced. In this case, the dishonest seller claims to sell the milk at cost price, which means he is selling it without any profit.
Percentage Gain:
The percentage gain is the profit percentage earned on the cost price. In this case, the dishonest seller is gaining 25% by mixing water with milk.
Now, let's solve the problem step by step:
Step 1: Assume the cost price of 1 liter of milk is 100 units. Since the seller claims to sell the milk at cost price, he is selling 1 liter of milk for 100 units.
Step 2: The dishonest seller mixes water to increase his profit. Let's assume he adds 'x' liters of water to 1 liter of milk. So, the total quantity of the mixture will be 1 + x liters.
Step 3: The dishonest seller gains 25% by mixing water with milk. This means that the selling price of the mixture is 125% of the cost price.
So, the selling price of the mixture is (125/100) * (100 + x) units.
Step 4: As the seller claims to sell the milk at cost price, the selling price should be equal to the cost price.
Therefore, we can write the equation as: (125/100) * (100 + x) = 100.
Step 5: Simplifying the equation, we have: (5/4) * (100 + x) = 100.
Step 6: Cross-multiplying, we get: 5(100 + x) = 4 * 100.
Step 7: Expanding the equation, we have: 500 + 5x = 400.
Step 8: Solving for 'x', we get: 5x = 400 - 500 = -100.
Step 9: Dividing both sides of the equation by 5, we get: x = -100/5 = -20.
Step 10: Since we cannot have a negative quantity of water, this result is not valid. Therefore, our assumption that the cost price is 100 units is incorrect.
Step 11: Let's try a different assumption for the cost price. Let's assume the cost price of 1 liter of milk is 'y' units.
Step 12: Following the same steps as above, we can write the equation as: (125/100) * (y + x) = y.
Step 13: Simplifying the equation, we have: (5/4) * (y + x) = y.
Step 14: Cross-multiplying, we get: 5(y + x) = 4y.
Step 15: Expanding the equation, we have: 5y + 5x = 4y.
Step 16: Simplifying the equation, we get:
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A dishonest seller professes to sell his milk at cost price but he mixes water with milk and gains 25 percent, then find the percentage of milk in the mixture.a)60%b)70%c)80%d)90%e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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