Question : Arbind has 650 kg of wheat. A part of which he sells at 9% profit and the rest at 19% profit to get 15% profit on the whole. What is the quantity (in kg) of wheat sold by Arbind at 9% profit?
Option 1: 260
Option 2: 195
Option 3: 455
Option 4: 390
Correct Answer: 260
Solution :
Let the quantity of wheat Arbind sells at 9% profit be $\text{x}$ kg.
The remaining quantity he sells at 19% profit is = $650 - \text{x}$ kg
The profit obtained from selling the first part at 9% profit is = $0.09\text{x}$ kg
The profit obtained from selling the second part at 19% profit is = $0.19(650 - \text{x})$ kg
According to the question,
$0.09\text{x} + 0.19(650 - \text{x}) = 0.15 \times 650$
$⇒0.09\text{x} + 0.19 \times 650 - 0.19\text{x} = 97.5$
$⇒-0.1\text{x} + 123.5 = 97.5$
$⇒-0.1\text{x} = -26$
$\therefore \text{x} = 260$
Hence the correct answer is 260 kg.
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