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 ratio of milk and water in the fourth container contains all the above three mixtures is

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

Answer 1

The correct option is C $157:53$

Let the volumes be $3x,4x,5x$ respectively.

Container with volume $3x$:

Milk $=\frac{4}{4+1}\times 3x$

Water $=\frac{1}{4+1}\times 3x$

Container with volume $4x$:

Milk $=\frac{3}{3+1}\times 4x$

Water $=\frac{1}{3+1}\times 4x$

Container with volume $5x$:

Milk $=\frac{5}{5+2}\times 5x$

Water $=\frac{2}{5+2}\times 5x$

Total milk $=\frac{12}{5}x+\frac{12}{4}x+\frac{25}{7}x=\frac{1256}{140}x$

Total water $=\frac{3}{5}x+\frac{4}{4}x+\frac{10}{7}x=\frac{424}{140}x$

Ratio of milk to water in 4th container $=\frac{1256}{424}=157:53$