In a zinc ore mine, 60 percent of the total mass consists of metals. Of this metallic portion, 3/4 percent is silver and the rest is zinc. If the total mass of ore extracted is 8,000 kg, what is the mass of zinc in kilograms?

Introduction / Context:
This question combines percentage composition with stepwise deduction. It asks you to work from the percentage of metals in the ore, then from that metallic portion identify how much is silver and finally how much is zinc. It is typical of mixture and composition questions often seen in aptitude exams.

Given Data / Assumptions:

• Total mass of ore = 8,000 kg.
• Metals form 60 percent of the ore by mass.
• Of the metallic portion, 3/4 percent is silver.
• The remainder of the metallic portion is zinc.

Concept / Approach:
First determine the total mass of metals by applying 60 percent to the total ore mass. Then find the amount of silver by applying 3/4 percent to the metallic mass. The zinc mass is simply the metallic mass minus the silver mass. This requires working with a very small percentage of a subset quantity, so careful calculation is important.

Step-by-Step Solution:
Step 1: Compute the mass of metals: 60 percent of 8,000 kg = (60 / 100) * 8,000 = 4,800 kg. Step 2: Silver is 3/4 percent of the metallic mass. Convert 3/4 percent to a fraction: 3/4 percent = (3 / 4) / 100 = 0.0075. Step 3: Silver mass = 0.0075 * 4,800 kg. Step 4: Compute 4,800 * 0.0075 = 36 kg of silver. Step 5: Zinc mass = total metallic mass − silver mass = 4,800 − 36 = 4,764 kg.

Verification / Alternative check:
We can confirm by checking that silver is a very small fraction. Since 1 percent of 4,800 kg is 48 kg, 0.75 percent (which is 3/4 percent) would be 0.75 * 48 = 36 kg, matching our computation. Subtracting 36 kg from 4,800 kg again yields 4,764 kg of zinc, so the result is consistent.

Why Other Options Are Wrong:

• 5,147 kg is greater than the total metallic mass of 4,800 kg, so it is impossible for zinc alone to weigh that much.
• 3,587 kg is too small and would imply an unrealistically large silver component.
• 2,125 kg is far below the correct value and does not arise from any reasonable calculation of the given percentages.

Common Pitfalls:
Learners may confuse 3/4 percent with 75 percent or with 3/4 of 60 percent, both of which are incorrect. Another common error is applying 3/4 percent directly to the total ore mass instead of the metallic portion. Always pay attention to which quantity a percentage is being applied to in multi-step problems.

Final Answer:
The mass of zinc in the ore is 4,764 kg.