Overall 20% profit with partial loss on one-fourth: A man buys sugar for ₹ 8000. He sells one-fourth at a 20% loss. At what profit percentage should he sell the remaining stock so that his overall profit is 20%?

Introduction / Context:
This problem blends partial loss and required overall profit. We compute the revenue from the loss-making portion and then determine the necessary gain on the remainder to hit the overall target.

Given Data / Assumptions:

• Total cost = ₹ 8000.
• One-fourth sold at 20% loss → cost of that portion = ₹ 2000.
• Overall target profit = 20% → total revenue target = 1.20 × 8000 = ₹ 9600.

Concept / Approach:
Compute revenue from the first (loss) portion, then find the required revenue from the remainder. Translate this to the needed profit percentage on the remaining cost base and express the answer as a clean percentage.

Step-by-Step Solution:
Revenue from first quarter = 0.80 × 2000 = ₹ 1600.Required revenue from remaining = 9600 − 1600 = ₹ 8000.Remaining cost = 8000 − 2000 = ₹ 6000.Required profit rate on remaining = (8000 − 6000) / 6000 = 2000 / 6000 = 1/3 = 33.33%.

Verification / Alternative check:
Check totals: Loss portion gives ₹ 1600; remainder at 33.33% gives ₹ 8000; sum = ₹ 9600 → exactly 20% overall profit on ₹ 8000 cost.

Why Other Options Are Wrong:

• 20% and 30% are too low; 40% is too high. Only 33.33% hits the exact overall target.

Common Pitfalls:

• Averaging percentages instead of using cost-weighted calculations.

Final Answer:
33.33%