A mixture is produced when we mix two or more quantities of different types of qualities. 

Simple Mixtures: When two different ingredients are mixed together, it is known as simple mixture, For example, a mixture of petrol and kerosene. 

Compound Mixtures: When two or more simple mixtures (Made of same ingredients of different proportions) are mixed together to form another mixture, it is known as a compound mixture. For example, a mixture containing milk and water in the ratio of 1:5 with another mixture containing milk and water in the ratio of 1:2

Two Mixtures (Alloys) of same ingredients mixed (compound mixtures)

Mixture 1 has ingredients A and B in the ratio \(a:b\) 

Mixture 2 has ingredients A and B  in the ratio \(c:d\)

If \(M\) units of Mixture 1 and \(N\) units of Mixture 2 are mixed to form a mixture containing the ingredients \(A\) and \(B\), the ratio of quantities of \(A\) and \(B\) in the resultant mixture is given by \[\color{blue}{\frac{{{Q_A}}}{{{Q_B}}} = \frac{{M \times \left( {\frac{a}{{a + b}}} \right) + N \times \left( {\frac{c}{{c + d}}} \right)}}{{M \times \left( {\frac{b}{{a + b}}} \right) + N \times \left( {\frac{d}{{c + d}}} \right)}}}\] 

The amount of ingredient \(A\) in the resultant mixture \(\color{blue}{ = \cfrac{{{Q_A}}}{{{Q_A} + {Q_B}}} \times (M + N)}\)

The amount of ingredient \(B\) in the resultant mixture \( \color{blue}{= \cfrac{{{Q_B}}}{{{Q_A} + {Q_B}}} \times (M + N)}\)

Example 01: 4 kg of a metal containing aluminum and silver in the ratio 2:1 is mixed with 5kg of another metal containing aluminum and silver in the ratio 4:3. What will be the ratio of aluminum to silver in the mixture? 

Solution: Here \(a:b=2:1, c:d = 4:3, M=4\) and \(N = 5\).

Substituting these values in the above formula, we get,

\(\cfrac{{{\rm{quantity}}\;{\rm{of}}\;{\rm{alumnium}}}}{{{\rm{quantity}}\;{\rm{of}}\;{\rm{silver}}}}\)\(= \cfrac{{4 \times \frac{2}{3} + 5 \times \frac{4}{7}}}{{4 \times \frac{1}{3} + 5 \times \frac{3}{7}}} = \cfrac{{\frac{{116}}{{21}}}}{{\frac{{73}}{{21}}}} = \frac{{116}}{{73}}\)