Question

In an alloy, iron, copper and silver are present in ratio \(7:3:1\). 660 kg of this alloy is taken, and 30 kg each of copper and silver is added to it. What will be the ratio of iron, copper and silver in the alloy after these additions?

• A. \(7:4:2\)
• B. \(14:7:1\)
• C. \(14:7:3\)
• D. \(7:3:3\)

Answer 1

The Correct Option is C

Alloy Ratio Calculation

- Initially, the ratio of iron, copper, and silver in the alloy is 7 : 3 : 1.

- The total quantity of alloy taken is 660 kg. Therefore, the amount of each metal in the initial mixture is calculated as follows:

• Iron: \[ \frac{7}{7 + 3 + 1} \times 660 = \frac{7}{11} \times 660 = 420 \text{ kg} \]
• Copper: \[ \frac{3}{11} \times 660 = 180 \text{ kg} \]
• Silver: \[ \frac{1}{11} \times 660 = 60 \text{ kg} \]

- After adding 30 kg of copper and 30 kg of silver, the new amounts become:

• Copper: 180 + 30 = 210 kg
• Silver: 60 + 30 = 90 kg

- The total weight of the new alloy is:

\[ 420 + 210 + 90 = 720 \text{ kg} \]

- The ratio of iron, copper, and silver in the new alloy is:

• Iron: 420 kg
• Copper: 210 kg
• Silver: 90 kg

- Simplifying the ratio:

\[ \text{Iron : Copper : Silver} = 420 : 210 : 90 = 14 : 7 : 3 \]

Conclusion: The correct answer is (c) 14 : 7 : 3.