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The average age of male employees in a firm is 52 years and that of female employees is 42 years. The mean age of all employees is 50 years. The percentage of male and female employees are respectively
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A) 80% and 20% |
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B) 20% and 80% |
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C) 50% and 50% |
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D) 52% and 48% |
Correct Answer:
| A) 80% and 20% |
Description for Correct answer:
Let the total male employees be m and total female employees be f
Now average age of male employees is 52 years
Total age of male employees = 52 m years and average age of female employees is 42 years
Total age of female employees = 42F years
Now mean age of all employees = 50 years
\( \Large \frac{52m + 42f}{f + m} = 50\)
52m + 42f = 50f + 50m
2m = 8f
m = 4f
Now % of male employee = \( \Large \left[ \frac{m}{m + f} \times 100 \right] \)%
= \( \Large \left[ \frac{4f}{4f + f} \times 100 \right] \)% (Here m = 4f)
\( \Large = \left[ \frac{4f}{5f} \times 100 \right] \)% = 80%
Now % of female employee = \( \Large \left[ \frac{m}{m + f} \times 100 \right] \)%
= \( \Large \left[ \frac{f}{4f + f} \times 100 \right] \)% (Here m = 4f)
\( \Large = \left[ \frac{1}{5} \times 100 \right] \)% = 20%
Let the total male employees be m and total female employees be f
Now average age of male employees is 52 years
Total age of male employees = 52 m years and average age of female employees is 42 years
Total age of female employees = 42F years
Now mean age of all employees = 50 years
\( \Large \frac{52m + 42f}{f + m} = 50\)
52m + 42f = 50f + 50m
2m = 8f
m = 4f
Now % of male employee = \( \Large \left[ \frac{m}{m + f} \times 100 \right] \)%
= \( \Large \left[ \frac{4f}{4f + f} \times 100 \right] \)% (Here m = 4f)
\( \Large = \left[ \frac{4f}{5f} \times 100 \right] \)% = 80%
Now % of female employee = \( \Large \left[ \frac{m}{m + f} \times 100 \right] \)%
= \( \Large \left[ \frac{f}{4f + f} \times 100 \right] \)% (Here m = 4f)
\( \Large = \left[ \frac{1}{5} \times 100 \right] \)% = 20%
Part of solved CDS Maths(2) questions and answers : Exams >> CDSE >> CDS Maths(2)
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