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Question 71
Two alloys A and B contain copper and zinc in the ratio 7 : 2 and 5 : 3 respectively. How many kg of A and B must be melted in order to get an alloy of 44 kg containing copper and Zinc in the ratio 3 : 1?
Solution
Copper in the A alloy=7/9
Copper in the B alloy=5/8
Copper in the resultant mixture=3/4
let the ratio in which they are mixed is x
By using the principle of allegation we have
x=((3/4)-(5/8))/((7/9)-(3/4))
x=(1/8)/(1/36)
x=9:2
Given 44 kg of mixture and so zinc copper present is (3/4)*44=33 kg
Therefore (7/9)*9y +(5/8)*2y =33
7y+(5y/4)=33
33y/4 =33
y=4
9y=36 kgs and 2y=8 kgs
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