Question : Three vessels whose capacities are 3 : 2 : 1 are filled with milk mixed with water. The ratio of milk and water in the mixture of vessels is 5 : 2, 4 : 1, and 4 : 1, respectively. Taking $\frac{1}{3}$ of first, $\frac{1}{2}$ of second, and $\frac{1}{7}$ of third mixtures, a new mixture kept in a new vessel is prepared. The percentage of water in the new mixture is:
Option 1: 28%
Option 2: 32%
Option 3: 30%
Option 4: 24%
Correct Answer: 24%
Solution :
Given: Three vessels whose capacities are 3 : 2 : 1 are filled with milk mixed with water.
The ratios of milk and water are 5 : 2, 4 : 1, and 4 : 1, respectively.
Let there be 105 litres in vessel 1, 70 litres in vessel 2, and 35 litres in vessel 3.
Amount of water after taking $\frac{1}{3}$ of first, $\frac{1}{2}$ of second and $\frac{1}{7}$ of third mixtures
= $105\times \frac{1}{3}\times \frac{2}{7}+70\times \frac{1}{2} \times \frac{1}{5}+35\times \frac{1}{7}×\frac{1}{5}$
= $10 + 7 + 1 = 18$ litres
Total volume of new mixture = $105\times \frac{1}{3}+70\times \frac{1}{2} +35\times \frac{1}{7}$ = 35 + 35 + 5 = 75 litres
$\therefore$ Percentage of water in the new mixture = $\frac{18}{75}$ × 100% = 24%
Hence, the correct answer is 24%.
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