A person has 1,000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% 'on the whole. The quantity sold at 18% profit is

Given:

A person has 1,000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole.

Formula used:

Let x be the quantity sold at 18% profit.

Total profit = (Quantity sold at 8% profit × 8%) + (Quantity sold at 18% profit × 18%)

Total sugar = 1000 kg

Average profit = 14%

Calculations:

Total profit = 1000 × 14%

⇒ 1000 × 0.14 = 140 kg

Let x be the quantity sold at 18% profit and (1000 - x) be the quantity sold at 8% profit.

0.08(1000 - x) + 0.18x = 140

⇒ 80 - 0.08x + 0.18x = 140

⇒ 80 + 0.10x = 140

⇒ 0.10x = 60

⇒ x = 600 kg

∴ The correct answer is option 3.