Question

Brass is an alloy of copper and zinc; bronze is an alloy containing 80 per cent of copper, 4 of zinc, and 16 of tin. A fused mass of brass and brozen is found to contain 74 per cent. of copper, 16 of zinc, and 10 of tin : find the ratio of copper to zinc in the composition of brass.

Answer 1

Given.

• Brass is an alloy of copper and zinc; bronze is an alloy containing 80 per cent of copper, 4 of zinc, and 16 of tin.

• A fused mass of brass and brozen is found to contain 74 per cent of copper, 16 of zinc, and 10 of tin.

To find.

• The ratio of copper to zinc in the composition of brass.

Solution.

Step 1. Assumption step

• Let the ratio of copper to zinc in the composition of brass be x : y.

• Also let m amount of brass alloy is fused with n amount of bronze alloy.

Step 2. Using amount of tin

• In brass alloy, copper : zinc = x : y
• Then in m mass, tin = 0, since there is no tin in brass alloy.

• In bronze alloy, copper : zinc : tin = 80 : 4 : 16
• Then in n mass, tin = 16/100 * n = 16n/100

• In fused alloy of brass and bronze, copper : zinc : tin = 74 : 16 : 10
• Then in (m + n) mass, tin = 10/100 * (m + n) = 10(m + n)/100

Step 3. Equating mass of tin

• Since there is a mass fusion, we can write
• 0 + 16n/100 = 10(m + n)/100
• or, 16n = 10m + 10n
• or, 10m = 6n
• or, m / n = 6 / 10
• or, m / n = 3 / 5

Step 4. Using amount of copper

• In brass alloy, copper : zinc = x : y
• Then in m mass, copper = m * x/100 = mx/100

• In bronze alloy, copper : zinc : tin = 80 : 4 : 16
• Then in n mass, copper = 80/100 * n = 80n/100

• In fused alloy of brass and bronze, copper : zinc : tin = 74 : 16 : 10
• Then in (m + n) mass, copper = 74/100 * (m + n) = 74(m + n)/100

Step 5. Equating mass of copper

• Since there is a mass fusion, we can write
• mx/100 + 80n/100 = 74(m + n)/100
• or, mx + 80n = 74m + 74n
• or, x + 80 (n/m) = 74 + 74 (n/m), since m ≠ 0
• or, x + 80 (5/3) = 74 + 74 (5/3), since m/n = 3/5
• or, x = 74 + 5/3 * (74 - 80)
• or, x = 74 + 5/3 * (- 6)
• or, x = 74 - 10
• or, x = 64
• Then y = 100 - 64 = 36

Step 6. Finding required ratio

• We have found, x = 64 and y = 36
• Thus, copper : zinc = 64 : 36

Answer.

• The ratio of copper to zinc in the composition of brass is 64 : 36.