Akshay has 1600 kg of sugar. He sells a part at 8% profit and the rest at 12% profit. If he gains 11% on the whole, find the quantity sold at 12%.A] 800 kg B] 1600 kg C] 1200 kg D] 1400 kg
Question
Akshay has 1600 kg of sugar. He sells a part at 8% profit and the rest at 12% profit. If he gains 11% on the whole, find the quantity sold at 12%.A] 800 kg B] 1600 kg C] 1200 kg D] 1400 kg
Solution
To solve this problem, we can use the method of weighted averages.
Step 1: Identify the weights and their respective values.
In this case, the weights are the quantities of sugar sold at 8% and 12% profit, and their respective values are 8 and 12.
Step 2: Set up the equation for the weighted average.
The weighted average is given by the formula:
(weight1 * value1 + weight2 * value2) / (weight1 + weight2) = average
In this case, the average is the overall profit, which is 11%.
Step 3: Substitute the known values into the equation.
Let the quantity of sugar sold at 8% profit be x kg. Then the quantity sold at 12% profit is (1600 - x) kg.
So, the equation becomes:
(x * 8 + (1600 - x) * 12) / 1600 = 11
Step 4: Solve the equation for x.
Solving the equation gives x = 800.
So, 800 kg of sugar was sold at 8% profit, and the rest, which is 1600 - 800 = 800 kg, was sold at 12% profit.
Therefore, the answer is A] 800 kg.
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