Alloy composition application: In a brass piece, the proportion of Zinc to Copper is 13 : 7 by weight. For a 100 kg piece of this brass, how many kilograms of Zinc are present?

Introduction / Context:
Ratio problems in mixtures and alloys translate directly into part-to-total calculations. If the composition by weight is known, the mass of a component is its ratio share over the total ratio sum times the total mass.

Given Data / Assumptions:

• Zinc : Copper = 13 : 7.
• Total mass of brass piece = 100 kg.

Concept / Approach:
Total ratio parts = 13 + 7 = 20. Zinc share = (13/20) of the total mass. Multiply by 100 kg to get kilograms of Zinc.

Step-by-Step Solution:

Verification / Alternative check:
Copper mass = (7/20) * 100 = 35 kg. 65 + 35 = 100 kg, confirming the partition.

Why Other Options Are Wrong:
20 kg and 55 kg understate the Zinc share; 70 kg would imply 14 : 6 ratio; 35 kg is actually the Copper portion.

Common Pitfalls:
Using 13% instead of the ratio fraction (13/20 = 65%); swapping component labels when interpreting the given order.

Final Answer:
65 kg