We have three alloys with different Copper to Zinc ratios:
• Alloy A: Cu:Zn =
1:2• Alloy B: Cu:Zn =
2:3• Alloy C: Cu:Zn =
1:4These are mixed in the ratio
2:3:5. We need to find the final Cu:Zn ratio.
Step 1: Convert ratios to fractionsIf Cu:Zn = a:b, then Copper fraction = a/(a+b)• Alloy A (1:2): Copper =
1/3, Zinc =
2/3• Alloy B (2:3): Copper =
2/5, Zinc =
3/5• Alloy C (1:4): Copper =
1/5, Zinc =
4/5Step 2: Calculate Copper contribution from each alloyWe take
2 parts of A,
3 parts of B, and
5 parts of C.
Copper from A = 2 × (1/3) =
2/3Copper from B = 3 × (2/5) =
6/5Copper from C = 5 × (1/5) =
1Total Copper = 2/3 + 6/5 + 1
Finding common denominator (15):
= 10/15 + 18/15 + 15/15 =
43/15Step 3: Calculate Zinc contribution from each alloyZinc from A = 2 × (2/3) =
4/3Zinc from B = 3 × (3/5) =
9/5Zinc from C = 5 × (4/5) =
4Total Zinc = 4/3 + 9/5 + 4
Finding common denominator (15):
= 20/15 + 27/15 + 60/15 =
107/15Step 4: Find the ratioCu : Zn = 43/15 : 107/15 =
43 : 107Answer: C