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Two alloys of zinc and copper are combined in the ratio 3 : 5 by volume. The resultant alloy is a 45% zinc alloy. What will be the proportion of zinc in the first alloy if the proportion of zinc in the second is 70%?

Two alloys of zinc and copper are combined in the ratio 3 : 5 by volume. The resultant alloy is a 45% zinc alloy. What will be the proportion of zinc in the first alloy if the proportion of zinc in the second is 70%? Correct Answer 3.33%

Using the rule of allegation, if two quantities are mixed, then

⇒ Quantity of zinc in first alloy/Quantity of zinc in second alloy = (Percentage of zinc in second alloy - Mean percentage)/(Mean percentage - Percentage of zinc in first alloy)

⇒ Substituting the values, Quantity of zinc in first alloy/Quantity of zinc in second alloy = (70 - 45)/(45 - x)

⇒ 25/(45 - x)

⇒ Given ratio = 3 : 5

⇒ 25/(45 - x) = 3/5

⇒ 25 × 5 = (45 – x) × 3

⇒ 25 × 5 = 135 - 3x

⇒ 3x = 135 - 125

⇒ 3x = 10

⇒ x = 10/3 = 3.33%

∴ Proportion of zinc in the first alloy = 3.33%

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