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Question : Three containers have their volumes in the ratio 3 : 4 : 5. They are full of mixtures of milk and water. The mixtures contain milk and water in the ratios (4 : 1), (3 : 1), and (5 : 2), respectively. The contents of all these three containers are poured into a fourth container. The ratio of milk and water in the fourth container is:

Option 1: 4 : 1

Option 2: 151 : 48

Option 3: 157 : 53

Option 4: 5 : 2


Team Careers360 9th Jan, 2024
Answer (1)
Team Careers360 12th Jan, 2024

Correct Answer: 157 : 53


Solution : Let the volumes of the three containers be $3x$, $4x$, and $5x$.
In the container with volume $3x$,
Milk $=\frac{4}{4+1}​×3x=\frac{12​x}{5}$
Water $=\frac{1}{4+1}​×3x=\frac{3​x}{5}$
In the container with volume $4x$,
Milk $=\frac{3}{3+1}​×4x=\frac{12​x}{4}​$
Water $= \frac{1}{3+1}​×4x=\frac{4x​}{4}​$
In the container with volume $5x$,
Milk $= \frac{5}{5+2}​×5x=\frac{25x​}{7}​$
Water $=\frac{2}{5+2}​×5x=\frac{10x​}{7}​$
Total milk $=\frac{12x​}{5}+\frac{12​x}{4}​+\frac{25x​}{7}​=\frac{336x+​420x+500x}{140}=\frac{1256x​}{140}$
Total water $=\frac{3x​}{5}+\frac{4​x}{4}​+\frac{10x​}{7}​=\frac{84x+140x+200x}{140}=\frac{424x​}{140}$
The ratio of milk to water in the 4 th container $=\frac{1256​}{424}​=157:53$
Hence, the correct answer is 157 : 53.

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