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. Find the quantity sold at 40% profit.

Question

Accepted Answer

Let the quantity sold at 10% profit be x kg, and at 40% profit be y kg. We know that x + y = 1000 kg. The overall profit is 20% on the whole.

Let the cost price per kg be Rs. 1 (for simplicity).

Total cost price = 1000 × 1 = Rs. 1000

Total selling price = x × 1.10 + y × 1.40

Overall profit = 20%, so total selling price = 1000 × 1.20 = Rs. 1200

So,
x × 1.10 + y × 1.40 = 1200
But x + y = 1000 ⇒ x = 1000 − y

Substitute:
(1000 − y) × 1.10 + y × 1.40 = 1200
1000 × 1.10 − y × 1.10 + y × 1.40 = 1200
1100 − 1.10y + 1.40y = 1200
1100 + 0.30y = 1200
0.30y = 1200 − 1100 = 100
y = 100 / 0.30 = 333.33 kg

So, the quantity sold at 40% profit is 333 1/3 kg.

Answer

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