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A merchant 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 18% profit.

A merchant 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 18% profit. Correct Answer 600kg

Let the C.P. of sugar be Rs. x per kg.Then, C.P. = Rs. 1000xLet the sugar sold at 8% gain by y kg.Then, sugar sold at 18% gain =(1000 − y) kg∴ (100108​ × xy) + [100118 ​× x(1000 − y)] = 100114 ​× 1000x⇒ 100108y ​+ 1180 − 100118y​ = 1140⇒ 10010y ​= 40⇒ y =400∴ Quantity sold at 18% gain =(1000 − 400) kg=600 kg.

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