There are two types of sugar. One is priced at Rs 62 per kg and the other is priced at Rs 72 per kg. If the two types are mixed together, the price of new mixture will be Rs 64.50 per kg. Find the ratio of the two types of sugar in this new mixture.
Question
There are two types of sugar. One is priced at Rs 62 per kg and the other is priced at Rs 72 per kg. If the two types are mixed together, the price of new mixture will be Rs 64.50 per kg. Find the ratio of the two types of sugar in this new mixture.
Solution
To solve this problem, we can use the method of alligation, which is a rule that allows us to find the ratio in which two or more ingredients at given prices must be mixed to produce a mixture of a desired price.
Here are the steps:
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Write down the prices of the two types of sugar: Rs 62 per kg and Rs 72 per kg.
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Write down the price of the mixture: Rs 64.50 per kg.
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Subtract the price of the cheaper sugar from the price of the mixture: 64.50 - 62 = Rs 2.50.
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Subtract the price of the mixture from the price of the more expensive sugar: 72 - 64.50 = Rs 7.50.
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The ratio of the two types of sugar in the new mixture is then given by the ratio of these two differences: 2.50 : 7.50.
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Simplify this ratio by dividing both sides by 2.50, we get 1 : 3.
So, the two types of sugar should be mixed in the ratio 1 : 3 to get a new mixture priced at Rs 64.50 per kg.
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