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?

The ratio of milk and water in mixture 1 is 3:5

Let the quantity of mixture-1 be x

Quantity of milk in mixture 1 \(= \frac{3}{8} * x = \frac{3x}{8}\)

Quantity of water in mixture 1\( = \frac{5}{8} * x = \frac{5x}{8}\)

The ratio of milk and water in mixture 2 is 6:1

Let the quantity of mixture-2 be y

Quantity of milk in mixture 2 \(= \frac{6}{7} * y = \frac{6y}{7}\)

Quantity of water in mixture 2 \(= \frac{1}{7} * x = \frac{y}{7}\)

Let us assume that the x quantity of mixture 1 and y quantity of mixture 2 are mixed together.

Therefore, the new ratio of milk and water will be = 1: 1.

Thus we get:

\(\frac{\frac{3x}{8}+\frac{6y}{7}}{\frac{5x}{8} + \frac{y}{7}} = 1\) \(\Rightarrow \frac{21 x + 48 y}{35 x + 8y} = 1\) \(\Rightarrow 21x + 48y = 35x + 8y\) \(\Rightarrow 21x – 35x = 8y – 48y\) \(\Rightarrow -14x = -40y\) \(\Rightarrow \frac{x}{y} = \frac{40}{14} = \frac{20}{7}\)

Therefore, the content of two glasses should be mixed in a ratio of 20:7

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