Ratio of the number of male employees to the total number of employees in a company is 5:8. If 200 female employees joined the company, then now the number of male employees in the company is 25% more than that of female employees, then find the number of female employees in the company finally?
- 800
- 500
- 1400
- None of these
The Correct Option is A
Solution and Explanation
Let's solve the problem step by step.
Initially, the ratio of the number of male employees to the total number of employees in the company is 5:8. Let the total number of employees be \(8x\). Then the number of male employees is \(5x\), and the number of female employees is \(8x-5x=3x\).
If 200 female employees join, the number of female employees becomes \(3x+200\).
We are given that the number of male employees is 25% more than that of the female employees. Therefore, the number of male employees, \(5x\), is 125% of the female employees. This can be expressed as:
\[ 5x = 1.25 \times (3x + 200) \]
Expanding this equation gives:
\[ 5x = 1.25 \times 3x + 1.25 \times 200 \]
\[ 5x = 3.75x + 250 \]
Subtract \(3.75x\) from both sides:
\[ 5x - 3.75x = 250 \]
\[ 1.25x = 250 \]
Dividing both sides by 1.25:
\[ x = \frac{250}{1.25} = 200 \]
Now we calculate the number of female employees finally:
The original number of female employees is \(3x=3 \times 200 = 600\).
After adding 200 female employees, the total number of female employees becomes:
\[ 600 + 200 = 800 \]
Thus, the final number of female employees in the company is 800.
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