Question : A trader had 1200 kg. of rice. He sold a part of it at 5% profit and the rest at 11% profit, so that he made a total profit of 7%. How much (In kg) rice did he sell at 5% profit?
Option 1: 900 Kg
Option 2: 600 Kg
Option 3: 400 Kg
Option 4: 800 Kg
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Correct Answer: 800 Kg
Solution :
Total amount of rice = 1200 kg
Total profit = 7%
Let the amount of rice he sold at 5% profit be $a$
Then, the amount of rice he sold at 11% profit will be $(1200-a)$
According to the question,
$a(1+\frac{5}{100})+(1200-a)(1+\frac{11}{100})=1200(1+\frac{7}{100})$
⇒ $1.05a+1.11(1200-a)=1200\times 1.07$
⇒ $0.06a=1200\times 0.04$
⇒ $a=800$
Hence, the correct answer is 800 Kg.
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