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 \(55 \frac{5}{9}\)%.**