A  and  B are two alloys of gold and copper prepared by mixing metals in proportional 7:2 and 7:11  respectively.  If equal quantities of alloys are melted to form a third alloy, 

then find the proportion of gold and copper in C .

We have to find the composition of copper and gold in the alloy C.

A and B are two alloys of gold and copper prepared by mixing metals in proportional 7:2 and 7:11 respectively.

Let x be the amount of each of component A and alloy B melted together to form C.

Amount of gold from A = 7x/(7+2) = 7x/9

Amount of gold from B = 7x/(7+11) = 7x/18

Total gold = 7x/9 + 7x/18 = 14x/18 + 7x/18 = 21x/18

Total copper = 2x - 21x/18 = 38x/18 - 21x/18 = 15x/18

Ratio of gold and copper in C

21x/36 : 15x/36

= 21x : 15x 

= 21 : 15 

= 7 : 5

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Let x be the amount of each of alloy A and alloy B melted together ( to form 2x of C)

Amount of gold from A = 7x/(7+2) = 7x/9

Amount of gold from B = 7x/(7+11) = 7x/18

Total gold = 7x/9 + 7x/18 = 14x/18 + 7x/18 = 21x/18

 

Total copper = 2x - 21x/18 = 38x/18 - 21x/18 = 15x/18

Ratio of gold and copper in C 

21x/36 : 15x/36

= 21x : 15x  =  21 : 15 = 7 : 5

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