1. Bottle 1 contains a mixture of milk and water in 7: 2 ratio and Bottle 2 contains a mixture of milk and water in 9: 4 ratio. In what ratio of volumes should the liquids in Bottle 1 and Bottle 2 be combined to obtain a mixture of milk and water in 3:1 ratio?
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By: anil on 05 May 2019 02.29 am
The ratio of milk and water in Bottle 1 is 7:2 and the ratio of milk and water in Bottle 2 is 9:4
Therefore, the proportion of milk in Bottle 1 is $$frac{7}{9}$$ and the proportion of milk in Bottle 2 is $$frac{9}{13}$$ Let the ratio in which they should be mixed be equal to X:1.
Hence, the total volume of milk is $$frac{7X}{9}+frac{9}{13}$$
The total volume of water is $$frac{2X}{9}+frac{4}{13}$$
They are in the ratio 3:1 Hence, $$frac{7X}{9}+frac{9}{13} = 3*(frac{2X}{9}+frac{4}{13})$$
Therefore, $$91X+81=78X+108$$
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Therefore, the proportion of milk in Bottle 1 is $$frac{7}{9}$$ and the proportion of milk in Bottle 2 is $$frac{9}{13}$$ Let the ratio in which they should be mixed be equal to X:1.
Hence, the total volume of milk is $$frac{7X}{9}+frac{9}{13}$$
The total volume of water is $$frac{2X}{9}+frac{4}{13}$$
They are in the ratio 3:1 Hence, $$frac{7X}{9}+frac{9}{13} = 3*(frac{2X}{9}+frac{4}{13})$$
Therefore, $$91X+81=78X+108$$
Therefore $$X = frac{27}{13}$$