Three vessels whose capacities are in the ratio 3 : 2 : 1 are completely filled with mixtures of milk and water. The ratios of milk to water in these vessels are 5 : 2, 4 : 1 and 4 : 1 respectively. A new mixture is made in a fresh vessel by taking \(\frac{1}{3}\) of the first, \(\frac{1}{2}\) of the second and \(\frac{1}{7}\) of the third mixture. What is the percentage of water in the new mixture?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 24
The percentage of water is total water ÷ total volume of the new mixture, so the volume and the water taken from each vessel are found separately.
Let the capacities be 3, 2 and 1 litres
From the first: \(\displaystyle \frac{1}{3}\times3=1\) litre, water \(\displaystyle =\frac{2}{7}\) litre
From the second: \(\displaystyle \frac{1}{2}\times2=1\) litre, water \(\displaystyle =\frac{1}{5}\) litre
From the third: \(\displaystyle \frac{1}{7}\times1=\frac{1}{7}\) litre, water \(\displaystyle =\frac{1}{5}\times\frac{1}{7}=\frac{1}{35}\) litre
Total volume \(\displaystyle =1+1+\frac{1}{7}=\frac{15}{7}\) litres
Total water \(\displaystyle =\frac{10}{35}+\frac{7}{35}+\frac{1}{35}=\frac{18}{35}\) litre
Water % \(\displaystyle =\frac{18}{35}\div\frac{15}{7}\times100=\frac{18}{75}\times100=24\%\)
The new mixture contains 24% water.