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