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Two alloys used to manufacture the third alloy. The first alloy contains Copper and Zinc only, and the second alloy contains Aluminium and Copper only. The Copper content in the two alloys is 40% and 60% respectively. The Zinc content in the new alloy should be between 30 to 40%. How much will be the minimum and maximum Copper content in the new alloy?

Two alloys used to manufacture the third alloy. The first alloy contains Copper and Zinc only, and the second alloy contains Aluminium and Copper only. The Copper content in the two alloys is 40% and 60% respectively. The Zinc content in the new alloy should be between 30 to 40%. How much will be the minimum and maximum Copper content in the new alloy? Correct Answer 46.67% and 50%

Calculation:

If x and y are the amounts of each alloy used for the manufacturing.

Copper in the new alloy = 0.4 x + 0.6 y

Copper content in the new alloy (in percentage) = ((0.4 x + 0.6 y)/(x + y)) × 100

Zinc in the new alloy = 0.6x

Zinc content in the new alloy (in percentage) = ((0.6x)/(x + y)) × 100

Zinc content should be in between 30 and 40%

30 ≤ ((0.6x)/(x + y)) × 100 ≤ 40

When, ((0.6x)/(x + y)) × 100 = 30

⇒ x = y

When, ((0.6x)/(x + y)) × 100 = 40

⇒ x = 2y

Copper content will be maximum when amount of first alloy is minimum. ie at x = y

⇒ Copper content = ((0.4 x + 0.6 y)/(x + y)) × 100

⇒ 50%

Copper content will be minimum when the amount of the first alloy is maximum. ie at x = 2y

⇒ 46.67%

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