Question

Three vessels having volumes in the ratio $2:3:5$ are full of a mixture of water and milk. In the first vessel ratio of water and milks is $1:3$, in second $2:3$ and in third vessel $2:5$. If all the three vessels were poured out in a large container, what is the resulting ratio of milk and water?

• A. $43:96$
• B. $438:962$
• C. $348:962$
• D. $481:219$

Answer 1

The correct option is D $481:219$

Ratio $2:3:5$

Ratio of milk : water

Vessel $13/41/4$

Vessel $23/52/5$

Vessel $35/72/7$

Quantity of water $=\frac{\frac{1}{4}\times 2x+\frac{2}{5}\times 3x+\frac{2}{9}\times 5x}{10x}$

$=\frac{x/2+6x/5+10x/7}{10x}$

$=\frac{5x+84x+100x}{700}=\frac{219}{700}$

Quantity of milk $=\frac{3/4\times 2x+3/5\times +5/7\times 5x}{10x}$

$=\frac{105x+126x+25x}{700}=\frac{480}{700}$

Ratio milk : Water $=481:219$

Option $\left(d\right)$ is correct.