Alloy Alligation (Brass – Copper:Zinc):\nTwo brass types have Cu:Zn = 8:3 and 15:7. If they are melted and mixed in the ratio 5:2 (by mass), what is Cu:Zn in the alloy?

Introduction / Context:
In alloys, component masses add. Compute total copper and zinc from each source, then simplify.

Given Data / Assumptions:

• Type A (8:3), total parts 11 ⇒ Cu = 8/11, Zn = 3/11.
• Type B (15:7), total parts 22 ⇒ Cu = 15/22, Zn = 7/22.
• Mass ratio A:B = 5:2.

Concept / Approach:
Take 5 units of A and 2 units of B. Add Cu and Zn contributions separately.

Step-by-Step Solution:
1) Cu = 5*(8/11) + 2*(15/22) = 40/11 + 15/11 = 55/11 = 5.2) Zn = 5*(3/11) + 2*(7/22) = 15/11 + 7/11 = 22/11 = 2.3) Ratio Cu:Zn = 5 : 2.

Verification / Alternative check:
Cross-checking with decimal fractions yields same ratio.

Why Other Options Are Wrong:
They stem from mixing denominators incorrectly or averaging ratios.

Common Pitfalls:
Forgetting to weight by the 5:2 mixing proportion.

Final Answer:
5 : 2