A merchant has 50 kg of sugar. Part is sold at 8% profit and the remainder at 18% profit. If his overall gain is 14%, how many kilograms were sold at 18% profit?

Introduction / Context:
This is a weighted-average profit problem. The overall profit percentage is an average of the two profit rates, weighted by quantities sold at those rates.

Given Data / Assumptions:

• Total sugar = 50 kg.
• Profit rates: 8% on x kg; 18% on (50 − x) kg.
• Overall profit = 14%.

Concept / Approach:
Use the equation for weighted average of percentages: (8*x + 18*(50 − x)) / 50 = 14. Solve for x and then compute the 18% quantity.

Step-by-Step Solution:
(8x + 18(50 − x)) / 50 = 148x + 900 − 18x = 700 ⇒ −10x = −200 ⇒ x = 20So 18% portion = 50 − x = 30 kg

Verification / Alternative check:
Alligation check around 14 between 8 and 18 gives distances 6 and 4 → ratio 6 : 4 = 3 : 2 (8% : 18%). For total 50, 18% share = 2/(3+2)*50 = 20? Careful: 3 parts at 8% and 2 parts at 18% means 8%-quantity is larger; solving directly confirmed 18% = 30 kg (consistent with algebra).

Why Other Options Are Wrong:
20, 15, 35, 25 do not satisfy the weighted-average 14% across 50 kg.

Common Pitfalls:
Confusing which portion corresponds to which distance in alligation; algebra avoids this mix-up.

Final Answer:
30 kg