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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?

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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


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Answered by on | Votes 2 |

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

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