Question : There are two containers of equal capacity. The ratio of milk to water in the first container is 3 : 1 and in the second container, 5 : 2. If they are mixed, the ratio of milk to water in the mixture will be:
Option 1: 28 : 41
Option 2: 41 : 28
Option 3: 15 : 41
Option 4: 41 : 15
Correct Answer: 41 : 15
Solution :
The ratio of milk to water is 3 : 1 in the first container.
Milk in the first container is $\frac{3}{4}$ litre-------------(i)
Water in the first container is $\frac{1}{4}$ litre-----------(ii)
The ratio of milk to water is 5 : 2 in the second container.
Milk in the second container is $\frac{5}{7}$ litre----------(iii)
Water in the second container is $\frac{2}{7}$ litre--------(iv)
For the final quantity of milk, adding equations (i) and (iii), we get,
$\frac{3}{4}+\frac{5}{7}=\frac{41}{28}$
For the final quantity of water, adding equations (ii) and (iv), we get,
$\frac{1}{4}+\frac{2}{7}=\frac{15}{28}$
$\therefore$ Final ratio of milk to water $=\frac{41}{28} :\frac{15}{28}=41:15$
Hence, the correct answer is 41 : 15.
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