Question

in one glass milk and water are mixed in ratio 3:5 and in another glass they are mixed in the ratio 6:1 in what ratio should the content of two of the two Glasses be mixed together so that the new mixture contains milk and water in the ratio 1:1​

Answer 1

Answer:

The content of two glasses should be mixed in ratio 20: 7

Step-by-step explanation:

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

$\frac{\frac{3x}{8} + \frac{6y}{7}}{\frac{5x}{8} + \frac{y}{7}} = \frac{1}{1}\\\\ \frac{\frac{21x}{56} + \frac{48y}{56}}{\frac{35x}{56} + \frac{8y}{56}} = 1\\\\ \frac{21x + 48y}{35x + 8y} = 1\\\\21x + 48y = 35x + 8y\\\\35x - 21x = 48y - 8y\\\\ 14x = 40y\\\\ \frac{x}{y} = \frac{40}{14}\\\\ \frac{x}{y} = \frac{20}{7}$

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