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 ratio of $(4:1),(3:1)$ 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 containers is

• A. $4:1$
• B. $151:48$
• C. $157:53$
• D. $5:2$

Answer 1

Answer: (C)

$157:53$

Let the volume of container is $3x,4x$ and $5x$

Given the mixtures milk and water in these container in the ratio $(4:1),(3:1)$ or $(5:2)$

Then volume of milk

$=3x\times \frac{4}{5}+\frac{3}{4}\times 4x+\frac{5}{7}\times 5x=\frac{12x}{5}+3x+\frac{25x}{7}=\frac{314}{35}$

Then volume of water

$=3x\times \frac{1}{5}+\frac{1}{4}\times 4x+\frac{2}{7}\times 5x=\frac{3x}{5}+x+\frac{10x}{7}=\frac{106}{35}$

Then ratio of milk and water

$=\frac{314}{35}:\frac{106}{35}=157:53$

Hence, option C is correct.