UGC NET Exam > UGC NET Questions > Two varieties of sugar A and B, costing Rs.40...
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Two varieties of sugar A and B, costing Rs.40 per kg and Rs. 50 per kg, respectively were mixed before selling. The mixture containing 500 kg of A, was sold with a gain of 10% for Rs.88,000. How many kilograms of B did the sold mixture contain?
- a)1200
- b)1300
- c)1400
- d)1500
Correct answer is option 'A'. Can you explain this answer?
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Two varieties of sugar A and B, costing Rs.40 per kg and Rs. 50 per kg...
Given Information:
- Cost of sugar variety A = Rs. 40 per kg
- Cost of sugar variety B = Rs. 50 per kg
- Mixture contains 500 kg of sugar variety A
- Selling price of the mixture = Rs. 88,000
- Gain = 10%
To find:
- How many kilograms of sugar variety B did the sold mixture contain?
Calculation:
1. Cost of the mixture:
- The cost of 1 kg of sugar variety A is Rs. 40, so the cost of 500 kg of sugar variety A is 500 * 40 = Rs. 20,000.
2. Selling price of the mixture:
- The selling price of the mixture is Rs. 88,000.
3. Gain:
- The gain percentage is 10%. This means the selling price is 10% more than the cost price.
- Gain = (10/100) * Cost Price
- 10/100 * Cost Price = Rs. 88,000 - Rs. 20,000
- 10/100 * Cost Price = Rs. 68,000
4. Cost Price of the mixture:
- Cost Price = (100/110) * Gain
- Cost Price = (100/110) * 68,000
- Cost Price = Rs. 62,000
5. Cost of sugar variety B in the mixture:
- The cost of 1 kg of sugar variety B is Rs. 50.
- Let the number of kilograms of sugar variety B in the mixture be x.
- The cost of x kg of sugar variety B is x * 50 = 50x
6. Cost of sugar variety A in the mixture:
- The cost of 500 kg of sugar variety A is Rs. 20,000.
7. Total cost of the mixture:
- Total cost = Cost of sugar variety A + Cost of sugar variety B
- Total cost = 20,000 + 50x
8. Equating the total cost and the cost price:
- Total cost = Cost Price
- 20,000 + 50x = 62,000
- 50x = 62,000 - 20,000
- 50x = 42,000
- x = 42,000 / 50
- x = 840
Therefore, the sold mixture contains 840 kg of sugar variety B.
Answer:
The correct option is (a) 1200.
- Cost of sugar variety A = Rs. 40 per kg
- Cost of sugar variety B = Rs. 50 per kg
- Mixture contains 500 kg of sugar variety A
- Selling price of the mixture = Rs. 88,000
- Gain = 10%
To find:
- How many kilograms of sugar variety B did the sold mixture contain?
Calculation:
1. Cost of the mixture:
- The cost of 1 kg of sugar variety A is Rs. 40, so the cost of 500 kg of sugar variety A is 500 * 40 = Rs. 20,000.
2. Selling price of the mixture:
- The selling price of the mixture is Rs. 88,000.
3. Gain:
- The gain percentage is 10%. This means the selling price is 10% more than the cost price.
- Gain = (10/100) * Cost Price
- 10/100 * Cost Price = Rs. 88,000 - Rs. 20,000
- 10/100 * Cost Price = Rs. 68,000
4. Cost Price of the mixture:
- Cost Price = (100/110) * Gain
- Cost Price = (100/110) * 68,000
- Cost Price = Rs. 62,000
5. Cost of sugar variety B in the mixture:
- The cost of 1 kg of sugar variety B is Rs. 50.
- Let the number of kilograms of sugar variety B in the mixture be x.
- The cost of x kg of sugar variety B is x * 50 = 50x
6. Cost of sugar variety A in the mixture:
- The cost of 500 kg of sugar variety A is Rs. 20,000.
7. Total cost of the mixture:
- Total cost = Cost of sugar variety A + Cost of sugar variety B
- Total cost = 20,000 + 50x
8. Equating the total cost and the cost price:
- Total cost = Cost Price
- 20,000 + 50x = 62,000
- 50x = 62,000 - 20,000
- 50x = 42,000
- x = 42,000 / 50
- x = 840
Therefore, the sold mixture contains 840 kg of sugar variety B.
Answer:
The correct option is (a) 1200.
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Community Answer
Two varieties of sugar A and B, costing Rs.40 per kg and Rs. 50 per kg...
Let the quantity of sugar B in the mixture be x kg.
Given, the mixture contains 500 kg of A
The cost of sugar A per kg is Rs. 40,
⇒ Total cost of sugar A in the mixture = 500 × 40 = Rs. 20,000.
Similarly, the cost of sugar B per kg is Rs. 50,
⇒ The total cost of sugar B in the mixture = x × 50 = Rs. 50x.
∴ The total cost of the mixture = Rs. (20,000 + 50x).
The mixture was sold for Rs. 88,000 with a 10% gain,
⇒ The selling price was 110% of the total cost.
⇒ 110% of (20,000 + 50x) = 88,000.
⇒1.1 × (20,000 + 50x) = 88,000.
⇒ 22,000 + 55x = 88,000.
⇒ 55x = 66,000.
⇒ x = 1,200.
∴ The mixture contained 1,200 kg of sugar B.
Given, the mixture contains 500 kg of A
The cost of sugar A per kg is Rs. 40,
⇒ Total cost of sugar A in the mixture = 500 × 40 = Rs. 20,000.
Similarly, the cost of sugar B per kg is Rs. 50,
⇒ The total cost of sugar B in the mixture = x × 50 = Rs. 50x.
∴ The total cost of the mixture = Rs. (20,000 + 50x).
The mixture was sold for Rs. 88,000 with a 10% gain,
⇒ The selling price was 110% of the total cost.
⇒ 110% of (20,000 + 50x) = 88,000.
⇒1.1 × (20,000 + 50x) = 88,000.
⇒ 22,000 + 55x = 88,000.
⇒ 55x = 66,000.
⇒ x = 1,200.
∴ The mixture contained 1,200 kg of sugar B.
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Two varieties of sugar A and B, costing Rs.40 per kg and Rs. 50 per kg, respectively were mixed before selling. The mixture containing 500 kg of A, was sold with a gain of 10% for Rs.88,000. How many kilograms of B did the sold mixture contain?a)1200b)1300c)1400d)1500Correct answer is option 'A'. Can you explain this answer?
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