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Alloy A contains metals x and y only in the ratio 5 : 2 and alloy B contains these metals in the ratio 3 : 4. Alloy C is prepared by mixing A and B in the ratio 4 : 5. The percentage of x in alloy C is:1. 45 %2. 56 %3. \(44 \frac{4}{9}\) %4. \(55 \frac{5}{9}\) % |
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Answer» Correct Answer - Option 4 : \(55 \frac{5}{9}\) % Given : The ratio of x and y in alloy A = 5 : 2 The ratio of x and y in alloy B = 3 : 4 The ratio of A and B in alloy C = 4 : 5 To find : Percentage of metal x in alloy C Calculation : Let the Quantity of metal x in alloy C be x ⇒ Quantity of metal x in alloy A = 5/7 ⇒ Quantity of metal y in alloy A = 2/7 ⇒ Quantity of metal x in alloy B = 3/7 ⇒ Quantity of metal y in alloy B = 4/7 A.T.Q., ⇒ The ratio of x and y in alloy C \( = \;\frac{{\left( {\frac{5}{7}} \right) × 4 + \left( {\frac{3}{7}} \right) × 5}}{{\left( {\frac{2}{7}} \right) × 4 + \left( {\frac{4}{7}} \right) × 5}}\) ⇒ The ratio of x and y in alloy C \( = \;\frac{{\frac{{20}}{7} + \frac{{15}}{7}}}{{\frac{8}{7} + \frac{{20}}{7}\;}}\) ⇒ The ratio of x and y in alloy C = 35/28 ⇒ Quantity of x in alloy C = 35/63 ⇒ Quantity of x in alloy C = 5/9 ⇒ Percentage of x in alloy C = (5/9) × 100 ∴ The percentage of x in alloy C is \(55 \frac{5}{9}\)%. |
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