Partial loss and partial gain on a fixed budget — overall percentage A man purchases sugar worth Rs 400. He sells 3/4 of it at a 10% loss and the remaining 1/4 at a 10% gain. What is his overall result as a percentage of cost?

Introduction / Context:
When equal-percent loss and gain are applied to different fractions of the same budget, compute the revenue from each part and compare the total with the original cost to find the overall percentage outcome.

Given Data / Assumptions:

• Total purchase (CP total) = Rs 400.
• 3/4 sold at 10% loss; 1/4 sold at 10% gain.
• Uniform cost per rupee of stock: portions are proportional in cost.

Concept / Approach:
Compute SP from each portion using its own percentage outcome and then sum: SP1 = 0.90 × CP1 and SP2 = 1.10 × CP2, where CP1 and CP2 are the corresponding portions of Rs 400.

Step-by-Step Solution:
CP1 = (3/4) × 400 = 300 ⇒ SP1 = 0.90 × 300 = 270.CP2 = (1/4) × 400 = 100 ⇒ SP2 = 1.10 × 100 = 110.Total SP = 270 + 110 = 380; Total CP = 400 ⇒ Net = −20 ⇒ −20/400 × 100 = −5%.

Verification / Alternative check:
Weighted average percentage = (0.75 × (−10%)) + (0.25 × (+10%)) = −7.5% + 2.5% = −5% (matches).

Why Other Options Are Wrong:
The other percentages do not match either the direct arithmetic or the weighted average calculation; 'no profit, no loss' is incorrect.

Common Pitfalls:
Taking the simple average of −10% and +10% (= 0%) without weighting by the portions, which is wrong.

Final Answer:
A loss of 5%