Q) An alloy of Copper, Zinc, Tin contains 91% copper, 6% zinc and 3% tin. A second alloy containing copper and tin only is fused with the first. The resulting alloy is found to contain 88% copper, 4.875% zinc and 7.125% tin. What is the proportion of copper and tin in the second alloy?
Answers
Answer:
75 % Copper & 25% Tin
Step-by-step explanation:
An alloy of Copper, Zinc, Tin contains 91% copper, 6% zinc and 3% tin. A second alloy containing copper and tin only is fused with the first. The resulting alloy is found to contain 88% copper, 4.875% zinc and 7.125% tin. What is the proportion of copper and tin in the second alloy
Let say First Alloy of 100A grams
First Alloy Contains Cu = 91A grams
Zinc = 6A gram
Tin = 3 A gram
Let say Second Contains Cu = C grams
= T gram
Second alloy total = C + T grams
Mixture will have copper = 91A + C grams
Zinc = 6A grams
Tin = 3A + T grams
Total = 91A + C + 6A + 3A + T = 100A + C + T grams
6A / (100A + C + T ) = 4.875/100
=> 600A = 487.5A + 4.875C + 4.875T
=> 112.5A = 4.875C + 4.875T
=> 300A = 13C + 13T
(91A + C) / (100A + C + T) = 88/100
=> 9100A + 100C = 8800A + 88C + 88T
=> 300A = 88T - 12C
13C + 13T = 88T - 12C
=> 25C = 75T
=> C = 3T
Total = C + T = 4T
Copper % = (3T/4T) * 100 = 75%
Tin % = (T/4T) * 100 = 25%
proportion of copper and tin in the second alloy = 75 % Copper & 25% Tin