In what ratio must rice at Rs. 9.30 per kg be mixed with rice at Rs. 10.80 per kg so that the mixture be worth Rs10 per kg? Options : 8:7 7:9 5:9 7:5
Question
In what ratio must rice at Rs. 9.30 per kg be mixed with rice at Rs. 10.80 per kg so that the mixture be worth Rs10 per kg?
Options : 8:7 7:9 5:9 7:5
Solution
To solve this problem, we can use the method of allegation, which is a rule of mixture to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of a desired price.
Here are the steps:
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Write down the cost of the cheaper and dearer ingredients on the left and right side respectively. In this case, Rs. 9.30 per kg (cheaper) and Rs. 10.80 per kg (dearer).
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Write down the mean value (the cost of the mixture) in the middle. In this case, Rs. 10 per kg.
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Calculate the differences between the mean value and the cost of the cheaper and dearer ingredients. The difference between Rs. 10 and Rs. 9.30 is Rs. 0.70, and the difference between Rs. 10.80 and Rs. 10 is Rs. 0.80.
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The required ratio of the mixture is the inverse of these differences. So, the ratio in which the two types of rice should be mixed is 0.80 : 0.70, which simplifies to 8 : 7.
So, the correct option is 8:7.
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