Weighted gain targeting — Out of 1000 kg of sugar, a merchant sells x kg at 8% profit and the rest at 18% profit to achieve an overall gain of 14%. How many kilograms are sold at 18% profit?

Introduction / Context:
This problem uses a weighted-average profit calculation. By setting up the total profit contribution from each portion and equating to the overall target percentage, we can solve for the quantity sold at the higher rate.

Given Data / Assumptions:

• Total quantity = 1000 kg.
• x kg at 8% profit; (1000 − x) kg at 18% profit.
• Overall profit = 14%.

Concept / Approach:
Total profit% on the whole = [0.08x + 0.18(1000 − x)] / 1000. Set equal to 0.14 and solve for x, then compute the amount at 18% which is (1000 − x).

Step-by-Step Solution:

Verification / Alternative check:
Check: profit from 400 kg at 8% = 32; from 600 kg at 18% = 108; total = 140 ⇒ 14% of 1000.

Why Other Options Are Wrong:
500, 400, 640, and 550 do not satisfy the overall 14% condition when substituted.

Common Pitfalls:
Averaging 8% and 18% directly without weights, or mixing up which part is x and which is (1000 − x).

Final Answer:
600 kg