A merchant has 1000 kg of sugar. Part is sold at 8% profit and the rest at 18% profit. Overall gain is 14%. How many kg were sold at 18% profit?

Problem restatement1000 kg are split across two profit rates (8% and 18%) to yield a 14% overall profit. Find the quantity at 18%.

Given data

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

Concept/ApproachUse weighted average of percentages by weight.

Step-by-step calculation (18x + 8(1000 − x)) / 1000 = 14 18x + 8000 − 8x = 14000 ⇒ 10x = 6000 ⇒ x = 600 kg

Verification/AlternativeAlligation check: distance from 14% to 8% is 6; from 18% to 14% is 4 ⇒ ratio at 8% : 18% = 4 : 6 = 2 : 3 ⇒ quantities 400 : 600 out of 1000 kg.

Common pitfalls

• Using selling prices instead of profit percentages; here base cancels in weighted average.

Final Answer600 kg