A merchant has 1000 kg of sugar, part of which he sells at a 10% profit and the rest at a 40% profit. He gains 20% on the whole. The quantity sold at 40% profit is:
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Correct answer: C
Explanation
The correct answer is Option 3 i.e. 333 kg.
Let the quantity of sugar sold at 40% profit be x kg
Therefore, the quantity of sugar sold at 10% profit will be (1000 - x) kg
The total profit made on the entire 1000 kg of sugar is 20%.
The merchant's gain on the total = 1000 × 20/100 = 200 kg
Now, the profit from selling x kg of sugar at 40% profit
Profit on x kg = x × 40/100 = 0.4x
And the profit from selling (1000 − x) kg at 10% profit
⇒&bsp;(1000 - x) × 10/100
⇒ 0.1(1000 - x)
The total profit is the sum of these two profits, which should equal 200
⇒ 0.4x + 0.1(1000 - x) = 200
⇒ 0.4x + 100 - 0.1x = 200
⇒ 0.3x = 100
⇒ x = 100/0.3
⇒ x = 1000/3 = 333.33 kg
Therefore, the quantity of sugar sold at 40% profit is 333 kg.