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Question

In one glass, milk and water are mixed in the ratio of 3:5 and in another glass they are mixed in the ratio 6:1. In what ratio should the content of the two glasses be mixed together so that the next mixture contains milk and water in the ratio of 1:1?

A
20:7
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B
8:3
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C
27:4
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D
25:9
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Solution

The correct option is A 20:7Ratio of milk and water in mixture 1 is 3:5Let quantity of mixture 1 be xQuantity of milk in mixture 1=38×x=3x8Quantity of water in mixture 1=58×x=5x8Ratio of milk and water in mixture 2 is 6:1Let quantity of mixture 2 be yQuantity of milk in mixture 2=67×y=6y7Quantity of water in mixture 2=17×x=y7Assume x quantity of mixture 1 and y quantity of mixture 2 is mixed.New ratio of milk and water =1:1Thus, we get3x8+6y75x8+y7=1⇒21x+48y35x+8y=1⇒21x+48y=35x+8y⇒21x−35x=8y−48y⇒−14x=−40y⇒xy=4014=207Thus, the content of two glasses should be mixed in ratio 20:7

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