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Question 3 : 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 ?

1. 27 : 14
2. 27 : 13
3. 27 : 16
4. 27 : 18

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Mixtures

Bottle 1 and bottle 2 contains mixture of milk and water in the ratio 7 : 2 and 9 : 4 respectively.
We have to find by what ratio bottle 1 and Bottle 2 should be combined to obtain a mixture of milk and water in the ratio 3 : 1
For this we can consider milk to the whole mixture or else water to the whole mixture.
⟹ \\frac{7}{9}) - \\frac{3}{4})
Taking LCM we get \\frac{28 - 27}{36}) = \\frac{1}{36})
⟹ \\frac{3}{4}) - \\frac{9}{13})
LCM is 52 so \\frac{39 - 36}{52}) = \\frac{3}{52})
\\frac{3}{52}) : \\frac{1}{36}) ⟹ \\frac{3}{52}) × \\frac{36}{1}) = 27 : 13
Bottle 1 and 2 are mixed in the ratio 27 : 13

The question is "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 ?"

Hence, the answer is 27 : 13

Choice B is the correct answer