Answer:
The requiired ratio of gold and silver in the final alloy mixture is[tex]= 9 : 11[/tex].
Explanation:
Concept:
The basic concept of alligation is similar to that of mixing, i.e. weighted average. Alligation helps to find the ratio in which two weights have to be mixed to obtain a given consistency of the mixture.
Given:
Quantity of first alloy[tex]=6[/tex]kg
Quantity of second alloy[tex]=18[/tex]kg
The ratio of gold and silver in first alloy[tex]=3 : 2[/tex]
The ratio of gold and silver in second alloy[tex]=2: 3[/tex]
Find:
We have to find the ratio of gold and silver in the final alloy mixture.
Solution:
The Quantity of gold in final alloy mixture is:
[tex]=\frac{6*3}{5}+\frac{18*2}{5}[/tex]
[tex]=\frac{18}{5}+\frac{36}{5}[/tex]
[tex]=3.6+7.2\\=10.8kg[/tex]
Quantity of silver in final alloy[tex]18+6=24kg[/tex] is,
[tex]=24-10.8\\=13.2kg[/tex]
The required ratio of gold and silver is,
[tex]=\frac{10.8}{13.2}\\ =\frac{9}{11}[/tex]
Thus, the ratio of gold and silver in the final alloy mixture[tex]= 9 : 11[/tex].