A shopkeeper sells one third of his goods at a profit of 10%, another one third at a profit of 20% and the remaining one third at a loss of 6%; what is his overall profit percentage on the entire stock?

Introduction / Context:
This question is about computing overall profit percentage when different parts of the same stock are sold at different profit or loss percentages. The shopkeeper divides his goods into three equal value parts and sells each part under different profit or loss conditions. The aim is to find the net profit percentage on the whole business. This scenario helps learners understand weighted averages in the context of profit and loss.

Given Data / Assumptions:

• The total stock is divided into three equal portions by cost value.
• First one third is sold at a profit of 10%.
• Second one third is sold at a profit of 20%.
• Third one third is sold at a loss of 6%.
• We assume the three parts have equal cost prices to simplify calculations.
• We need the overall profit percentage on total cost of all goods.

Concept / Approach:
Because each portion is one third of the total cost value, the overall profit percentage can be found by taking the simple average of the three individual profit or loss percentages. In general, when identical cost bases are used, overall profit percentage is the arithmetic mean of component percentages. So we simply average 10%, 20% and -6%. Alternatively, we can assume a convenient total cost, compute each part cost, find total selling price and then derive profit percentage.

Step-by-Step Solution:
Step 1: Let total cost price of all goods be Rs. 300 for easy calculations.Step 2: Then each one third portion has cost price = 300 / 3 = Rs. 100.Step 3: For the first portion, profit = 10% of 100 = Rs. 10, so selling price = 110.Step 4: For the second portion, profit = 20% of 100 = Rs. 20, so selling price = 120.Step 5: For the third portion, loss = 6% of 100 = Rs. 6, so selling price = 94.Step 6: Total selling price = 110 + 120 + 94 = Rs. 324.Step 7: Total cost price = Rs. 300 by assumption.Step 8: Net profit = 324 - 300 = Rs. 24.Step 9: Overall profit percentage = (24 / 300) * 100.Step 10: Simplify 24 / 300 = 0.08, so profit percentage = 8%.

Verification / Alternative check:
Since each third has equal cost value, we can simply average the three percentages directly: (10 + 20 - 6) / 3. Sum of percentages = 24. Divide by 3 to get 8%. This quick method gives the same result as the detailed calculation above. Therefore, the overall profit percentage is confirmed to be 8%.

Why Other Options Are Wrong:

• 6%: This might be guessed by subtracting the loss directly from one of the profits, but it ignores the actual distribution of gains and losses.
• 10%: This is just one of the individual profits, not the combined effect.
• 12%: This value overstates the profit and does not arise from any correct averaging or total calculation.

Common Pitfalls:

• Forgetting that the loss is on one third of the goods and treating it as if it reduces one particular profit directly.
• Using an incorrect weighted average when the parts are actually equal in cost.
• Confusing profit percentages on cost with percentages on selling price, which would change the computation completely.

Final Answer:
The shopkeeper overall makes a profit of 8% on the entire stock of goods.