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How many kg of sugar costing Rs. 5.75 per kg should be mixed with 75 kg of cheaper sugar costing Rs. 4.50 per kg so that the mixture is worth Rs. 5.50 kg?
- a)350 kg
- b)300 kg
- c)250 kg
- d)325 kg
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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To solve this problem, we can use the concept of weighted averages.
Let x be the amount of sugar costing Rs. 5.75 per kg that needs to be mixed with 75 kg of cheaper sugar costing Rs. 4.50 per kg.
The cost per kg of the mixture is given as Rs. 5.50. Therefore, the total cost of the mixture can be calculated as follows:
Total cost = (cost of sugar costing Rs. 5.75 per kg * x) + (cost of cheaper sugar costing Rs. 4.50 per kg * 75)
Since the mixture is worth Rs. 5.50 per kg, the total cost divided by the total amount of sugar in the mixture should also be equal to Rs. 5.50 per kg.
Total cost / (x + 75) = 5.50
Simplifying this equation, we get:
5.75x + 4.50 * 75 = 5.50 * (x + 75)
5.75x + 337.50 = 5.50x + 412.50
0.25x = 75
x = 300 kg
Therefore, 300 kg of sugar costing Rs. 5.75 per kg should be mixed with 75 kg of cheaper sugar costing Rs. 4.50 per kg in order to obtain a mixture worth Rs. 5.50 per kg. Hence, the correct answer is option B.
Let x be the amount of sugar costing Rs. 5.75 per kg that needs to be mixed with 75 kg of cheaper sugar costing Rs. 4.50 per kg.
The cost per kg of the mixture is given as Rs. 5.50. Therefore, the total cost of the mixture can be calculated as follows:
Total cost = (cost of sugar costing Rs. 5.75 per kg * x) + (cost of cheaper sugar costing Rs. 4.50 per kg * 75)
Since the mixture is worth Rs. 5.50 per kg, the total cost divided by the total amount of sugar in the mixture should also be equal to Rs. 5.50 per kg.
Total cost / (x + 75) = 5.50
Simplifying this equation, we get:
5.75x + 4.50 * 75 = 5.50 * (x + 75)
5.75x + 337.50 = 5.50x + 412.50
0.25x = 75
x = 300 kg
Therefore, 300 kg of sugar costing Rs. 5.75 per kg should be mixed with 75 kg of cheaper sugar costing Rs. 4.50 per kg in order to obtain a mixture worth Rs. 5.50 per kg. Hence, the correct answer is option B.
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How many kg of sugar costing Rs. 5.75 per kg should be mixed with 75 kg of cheaper sugar costing Rs. 4.50 per kg so that the mixture is worth Rs. 5.50 kg?a)350 kgb)300 kgc)250 kgd)325 kge)None of theseCorrect answer is option 'B'. Can you explain this answer?
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