In a glass, milk and water are mixed in the ratio of 3:5 and in another glass they are mixed in the ratio of 6

Question

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

Accepted Answer

Let's use the fraction of milk in each mixture to apply Alligation.
* Milk fraction in 1st glass (

m_{1}

) =

\frac{3}{3 + 5} = \frac{3}{8}

* Milk fraction in 2nd glass (

m_{2}

) =

\frac{6}{6 + 1} = \frac{6}{7}

* Milk fraction in final mixture (

m_{m}

) =

\frac{1}{1 + 1} = \frac{1}{2}

Applying the Alligation rule:

Left difference = m_{2} - m_{m} = \frac{6}{7} - \frac{1}{2} = \frac{12 - 7}{14} = \frac{5}{14}

Right difference = m_{m} - m_{1} = \frac{1}{2} - \frac{3}{8} = \frac{4 - 3}{8} = \frac{1}{8}

The required mixing ratio is:

Ratio = \frac{5}{14} : \frac{1}{8}

Multiply both sides by

56

(

LCM

of 14 and 8):

Ratio = (\frac{5}{14} \times 56) : (\frac{1}{8} \times 56) = 20 : 7

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

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