Question : Three containers whose volumes are in the ratio of 2 : 3 : 4 are full of a mixture of spirit and water. In the 1st container, the ratio of spirit and water is 4 : 1, in the second container the ratio is 11 : 4 and in the 3rd container the ratio is 7 : 3. All three mixtures are mixed in a big container. The ratio of spirit and water in the resultant mixture is:
Option 1: 4 : 9
Option 2: 11 : 4
Option 3: 5 : 10
Option 4: 9 : 5
Correct Answer: 11 : 4
Solution :
Given: Three containers whose volumes are in the ratio of 2 : 3 : 4 are full of a mixture of spirit and water.
In 1st container, the ratio of spirit and water is 4 : 1, in the second is 11 : 4 and in 3rd is 7 : 3.
Let the volumes of three containers be $2k, 3k,$ and $4k,$ respectively.
In the first container:
Spirit = $2k×\frac{4}{5}=\frac{8k}{5}$
Water = $2k×\frac{1}{5}=\frac{2k}{5}$
In the second container:
Spirit = $3k×\frac{11}{15}=\frac{11k}{5}$
Water = $3k×\frac{4}{15}=\frac{4k}{5}$
In the 3rd container:
Spirit = $4k×\frac{7}{10}=\frac{14k}{5}$
Water = $4k×\frac{3}{10}=\frac{6k}{5}$
So, required ratio = $(\frac{8k}{5}+\frac{11k}{5}+\frac{14k}{5}):(\frac{2k}{5}+\frac{4k}{5}+\frac{6k}{5})=(\frac{33k}{5}):(\frac{12k}{5})= 33:12 = 11:4$
Hence, the correct answer is 11 : 4.
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