Question

Somaiah has a mixture of milk and water in the ratio of 8:7 and Ramaiah has the same in the ratio of 5:9. In what ratio should these two be mixed so that the required ratio of milk and water is 1:1?

Answer 1

Somaiah has a mixture of milk and water in the ratio of 8:7 and Ramaiah has the same in the ratio of 5:9. In what ratio should these two be mixed so that the required ratio of milk and water is 1:1?

Solution:

Suppose we must take $x$ (units) of Somaiah's mixture and $y$ (units) of Ramaiah's one. Thus we have

1. In Somaiah's mixture: milk is $\frac{8}{8 + 7} x = \frac{8}{15} x$ (units); water is $\frac{7}{15} x$ (units).

2. In Ramaiah's mixture: milk is $\frac{5}{9 + 5} y = \frac{5}{14} y$ (units); water is $\frac{9}{14} y$ (units).

Because (by the condition of the task) the required ratio of milk and water is 1:1 then

milk of Somaiah's mixture+milk of Ramaiah's mixture=water of Somaiah's mixture+water of Ramaiah's mixture,

$$\begin{array}{l} \frac{8}{15} x + \frac{5}{14} y = \frac{7}{15} x + \frac{9}{14} y, \\ \frac{8}{15} x - \frac{7}{15} x = \frac{9}{14} y - \frac{5}{14} y, \\ \frac{1}{15} x = \frac{4}{14} y, \\ \frac{x}{y} = \frac{2}{7} \div \frac{1}{15}, \\ \frac{x}{y} = \frac{30}{7}. \end{array}$$

Answer: The ratio of these two mixed is 30 to 7.