In an ornament, the ratio of gold to copper is 3 : 2. Based on this ratio, what percentage of the total metal in the ornament is gold?

Introduction / Context: In many aptitude and quantitative exams, questions on ratios and percentages test a learner's ability to convert a given ratio into a percentage of the whole. This question talks about an ornament made of gold and copper mixed in a specific ratio and asks what percentage of the ornament is gold. Understanding the basic idea that a ratio compares parts of a whole is the key to solving such questions quickly and accurately.

Given Data / Assumptions:

• The ornament is made of gold and copper only.
• The ratio of gold to copper is 3 : 2.
• No other metal is mixed in the ornament.
• We are required to find the percentage of gold in the entire ornament.

Concept / Approach: The ratio 3 : 2 means that out of a total of 3 + 2 equal parts, 3 parts are gold and 2 parts are copper. To convert a ratio part into a percentage, we divide the required part by the total number of parts and then multiply by 100. So, percentage of gold = (gold parts / total parts) * 100. This approach works even if the actual total mass or volume of the ornament is not given, because the ratio already expresses the relative composition.

Step-by-Step Solution: Step 1: Identify the number of parts for each metal. Gold = 3 parts, copper = 2 parts. Step 2: Calculate the total number of parts in the ornament. Total parts = 3 + 2 = 5. Step 3: Express the fraction of gold as gold parts divided by total parts. Fraction of gold = 3 / 5. Step 4: Convert this fraction into a percentage. Percentage of gold = (3 / 5) * 100. Step 5: Simplify the calculation. (3 / 5) * 100 = 60. Step 6: Therefore, gold constitutes 60 percent of the ornament.

Verification / Alternative check: An alternative way is to imagine a convenient total quantity for the ornament. For example, assume the total weight is 5 grams to match the total parts (3 + 2). Then gold would be 3 grams and copper would be 2 grams. Percentage of gold = (3 / 5) * 100 = 60. This confirms the earlier calculation and shows that the answer is independent of the actual total mass, because the ratio remains the same.

Why Other Options Are Wrong: 60 is correct because it equals 3 parts out of 5 in percentage form. Option 40 would correspond to copper, not gold. Option 30 and option 20 are smaller fractions and do not match 3 out of 5. Therefore, these values cannot represent the percentage of gold in the ornament.

Common Pitfalls: A common mistake is to treat one of the ratio numbers directly as a percentage. For example, some learners might incorrectly say that gold is 3 percent, which ignores the total number of parts. Another error is to forget to add the parts when calculating the total. Always remember that ratios indicate parts of a whole, and the percentage must be computed with respect to the sum of all parts.

Final Answer: The percentage of gold in the ornament is 60 percent.