Question

The contents of two vessels containing water and milk in the ratio 1 : 2 and 2 : 5 are mixed in the ratio 1 : 4 The resulting mixture will have water and milk in the ratio

• A. 30 : 75
• B. 31 : 74
• C. 31 : 75
• D. 30 : 74

Answer 1

The correct option is B 31 : 74

Let the first mixture be A.

Then A$\equiv$water:milk=1:2, &

Let the second mixture be B.

Then B$\equiv$water:milk=2:5.

So in A the amount of milk=$\frac{2}{1+2}$part=$\frac{2}{3}$part

and in B the amount of milk=$\frac{5}{2+5}$part=$\frac{5}{7}$part.

Similarly, in A the amount of water=$\frac{1}{1+2}$part=$\frac{1}{3}$part

and in B the amount of water=$\frac{2}{2+5}$part=$\frac{2}{7}$part.

Now, in the new mixture A:B=1:4.

So the quantity of mixture A=$1\times A=1\times \frac{2}{3}$ part milk=$=\frac{2}{3}$part milk and

$1\times \frac{1}{3}$patrt water=$\frac{1}{3}$part of water.

Similarly, the quantity of mixture B=$4\times B=4\times \frac{5}{7}$ part milk=$=\frac{20}{7}$part milk and

$4\times \frac{2}{7}$ part water=$\frac{8}{7}$part of water.

Then the total quantity of milk in the new mixture=$\frac{2}{3}+\frac{4}{7}$part

=$\frac{74}{21}$part .

Again the total quantity of water in the new mixture=$\frac{1}{3}+\frac{8}{7}$part

=$\frac{31}{21}$part .

So, in the new mixture,

water : milk=$\frac{31}{21}:\frac{74}{21}$=31 : 74.

Ans- Option B.