A shopkeeper makes varying profits on selling certain amount of sugar weighing 84 kgs. On certain part of the total quantity, he makes a profit of 9% profit and rest at 16% profit. If the overall gain for the shopkeeper is 12% profit on the whole quantity, then find how much is sold at 16% profit?
1). 36 kgs
2). 48 kgs
3). 66 kgs
4). None of these
Using the rule of allegation, if two quantities are mixed, then
⇒ Quantity of first part/Quantity of second part = (Profit percentage of second part – Mean Profit)/(Mean profit percentage – Profit percentage of first part)
⇒ Substituting the values, Quantity of first part/Quantity of second part = (16 – 12)/(12 – 9)
⇒ Quantity of first part/Quantity of second part = 4/3
⇒ Ratio is 4 : 3
⇒ Quantity sold at 16% profit = [3/(4 + 3)] × 84 kg
⇒ (3/7) × 84 kg
⇒ 36 kg
∴ Quantity sold at 16% profit = 36 kgs