Question

In one glass, milk and water are mixed in the ratio of 3:5 and in another glass they are mixed in the ratio 6:1. In what ratio should the content of the two glasses be mixed together so that the next mixture contains milk and water in the ratio of 1:1?

• A. 20:7
• B. 8:3
• C. 27:4
• D. 25:9

Answer 1

The correct option is A 20:7

Ratio of milk and water in mixture $1$ is $3:5$

Let quantity of mixture $1$ be $x$

Quantity of milk in mixture $1=\frac{3}{8}\times x=\frac{3x}{8}$

Quantity of water in mixture $1=\frac{5}{8}\times x=\frac{5x}{8}$

Ratio of milk and water in mixture $2$ is $6:1$

Let quantity of mixture $2$ be $y$

Quantity of milk in mixture $2=\frac{6}{7}\times y=\frac{6y}{7}$

Quantity of water in mixture $2=\frac{1}{7}\times x=\frac{y}{7}$

Assume $x$ quantity of mixture $1$ and $y$ quantity of mixture $2$ is mixed.

New ratio of milk and water $=1:1$

Thus, we get

$\frac{\frac{3x}{8}+\frac{6y}{7}}{\frac{5x}{8}+\frac{y}{7}}=1$

$\Rightarrow \frac{21x+48y}{35x+8y}=1$

$\Rightarrow 21x+48y=35x+8y$

$\Rightarrow 21x-35x=8y-48y$

$\Rightarrow -14x=-40y$

$\Rightarrow \frac{x}{y}=\frac{40}{14}=\frac{20}{7}$

Thus, the content of two glasses should be mixed in ratio $20:7$