Alloy A contains 40% gold and 60% silver. Alloy B contains 35% gold, 40% silver and 25% copper. If alloys A and B are mixed in the ratio 1 : 4 by weight, what are the respective percentages of gold and silver in the newly formed alloy?

Introduction / Context:
This question is about mixing two alloys with known percentage compositions to form a new alloy. It tests understanding of weighted averages and percentage calculations when different components like gold, silver and copper are involved.

Given Data / Assumptions:

• Alloy A: 40% gold and 60% silver.
• Alloy B: 35% gold, 40% silver and 25% copper.
• Alloys A and B are mixed in the ratio 1 : 4 by weight.
• We must find the percentage of gold and the percentage of silver in the new alloy.

Concept / Approach:
Assume convenient total weights for the alloys according to the given mixing ratio, for example 1 kg of alloy A and 4 kg of alloy B. Compute the mass of gold and silver from each alloy using the given percentages. Add the masses and then express them as percentages of the total mass of the new alloy. Copper is present but only gold and silver percentages are required.

Step-by-Step Solution:
Step 1: Assume we mix 1 kg of alloy A and 4 kg of alloy B (total 5 kg). Step 2: In 1 kg of alloy A, gold = 40% of 1 kg = 0.40 kg and silver = 60% of 1 kg = 0.60 kg. Step 3: In 4 kg of alloy B, gold = 35% of 4 kg = 0.35 * 4 = 1.40 kg. Step 4: In 4 kg of alloy B, silver = 40% of 4 kg = 0.40 * 4 = 1.60 kg. Step 5: Total gold in new alloy = 0.40 + 1.40 = 1.80 kg. Step 6: Total silver in new alloy = 0.60 + 1.60 = 2.20 kg. Step 7: Total mass of new alloy = 1 + 4 = 5 kg. Step 8: Percentage of gold = (1.80 / 5) * 100 = 36%. Step 9: Percentage of silver = (2.20 / 5) * 100 = 44%.

Verification / Alternative check:
Gold percentage 36 and silver percentage 44 sum to 80%. The remaining 20% of the alloy must be copper, which is consistent with the fact that only alloy B originally contained copper and that it occupied 25% of B but only four fifths of the total mixture is B. Thus the distribution is internally consistent and the calculations are correct.

Why Other Options Are Wrong:
Options such as 20% and 30% or 25% and 35% would imply total gold and silver percentages far below the 75 to 80 percent range implied by the original compositions, which is not possible given that alloy A has 100% gold and silver and alloy B has 75% gold and silver combined. Only 36% and 44% align with the weighted contribution from each alloy.

Common Pitfalls:
A common mistake is to average the percentages directly as (40 + 35) / 2 without weighting by the mixing ratio 1 : 4. Another error is to forget that the total alloy mass changes when mixing, so gold and silver percentages must be taken over the total 5 parts, not individually. Careless handling of percentage to mass conversion also causes confusion, so always express quantities explicitly in kilograms or grams before computing final percentages.

Final Answer:
In the new alloy, gold is 36% and silver is 44% by weight.