A Shopkeeper has 1000 kg of sugar, part of which he sells at 8% and the remaining at 18% profit. He gains 14% on the whole. Find the quantity of sugar that he sold at 8% profit.

Question: A Shopkeeper has 1000 kg of sugar, part of which he sells at 8% and the remaining at 18% profit. He gains 14% on the whole. Find the quantity of sugar that he sold at 8% profit.

Solution:
Let,
The cost price of sugar be tk. x per kg
∴ Total cost price = Tk. 1000x
The sugar sold at 8% gain by y kg
The sugar sold at 18% gain by (1000 - y) kg

Now
{(108xy)/100} + [{118x(1000 - y)}/100] = (114/100) × (1000x)
⇒ (108y)/100 + [{118(1000 - y)}/100] = (114 × 1000)/100
⇒ 108y + {118(1000 - y)} = 114 × 1000
⇒ 108y + 118000 - 118y = 114000
⇒ 118000 - 114000 = 10y
⇒ 4000 = 10y
∴ y = 400 kg