Question : The average monthly salary of all the employees in a factory is Rs. 8840. If the average salary of all the officers is Rs. 15000 and that of the remaining employees is Rs. 8000, what is the percentage of the officers among the employees?
Option 1: $10\%$
Option 2: $12\%$
Option 3: $8\frac{1}{3}\%$
Option 4: $11\%$
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Correct Answer: $12\%$
Solution :
Let the number of officers = $x$ and non-officers = $y$
Total salary of officers = Rs. $15000x$
Total salary of non-officers = Rs. $8000y$
According to the question,
$15000x + 8000y = 8840(x+y)$
⇒ $15000x - 8840x=8840y- 8000y$
⇒ $6160x =840y$
⇒ $x:y=3:22$
So, the percentage of the officers among the employees
$=\frac{x}{x+y}\times 100=\frac{3}{3+22}\times 100 =\frac{3}{25}\times 100= 12\%$
Hence, the correct answer is $12\%$.
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