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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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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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