Directions: Study the table given below carefully and answer the question that follows.

The table displays the total workforce and the percentage of female employees across four different company branches.

Note: The number of male employees in Branch P is 700, and the total number of female employees in Branches Q and S together is 945.

$\begin{array}{ccc}\text{Branch}& \text{Total workforce}& \text{Percentage of females}\\ P& 800& X\%\\ Q& 1200& 60\%\\ R& 500& 40\%\\ S& 900& Y\%\end{array}$

In Branch P, the ratio of male employees who work in the government sector to those who work in the private sector is 3:4, while the total number of employees working in the private sector is 18Y. Find the ratio of the total number of female employees in the private sector to those in the government sector.

The correct answer is 1:1.

From the given table, we have the following workforce data across different branches:
- Branch P: Total workforce = 800, Percentage of females = X%
- Branch Q: Total workforce = 1200, Percentage of females = 60%
- Branch R: Total workforce = 500, Percentage of females = 40%
- Branch S: Total workforce = 900, Percentage of females = Y%

Step 1: Find the number of female employees in Branch P.

Given that the number of male employees in Branch P is 700 and the total workforce is 800:

$\text{Total female employees in Branch P}=800-700=100$

Step 2: Calculate the number of female employees in Branch Q.

Branch Q has a total workforce of 1200, with 60% female employees:

$\text{Female employees in Branch Q}=60\%\text{of}1200=\frac{60}{100}*1200=720$

Step 3: Calculate the number of female employees in Branch S and determine the value of Y.

The total number of female employees in Branches Q and S together is 945:

$\text{Female employees in Branch S}=945-720=225$

Since the percentage of females in Branch S is Y% of 900:

$\frac{Y}{100}*900=225$

$9Y=225$

$Y=25$

Step 4: Determine the number of male employees in the Government and Private sectors in Branch P.

The total male employees in Branch P is 700. The ratio of male employees working in the government sector to the private sector is 3:4.

Total parts = 3 + 4 = 7 parts.

$\text{Male employees in Government sector}=\frac{3}{7}*700=300$

$\text{Male employees in Private sector}=\frac{4}{7}*700=400$

Step 5: Find the number of female employees in the Private and Government sectors in Branch P.

The total number of employees working in the private sector in Branch P is 18Y:

$\text{Total employees in Private sector}=18*25=450$

Subtracting male employees in the private sector from the total private sector workforce gives:

$\text{Female employees in Private sector}=450-400=50$

Since the total number of female employees in Branch P is 100:

$\text{Female employees in Government sector}=100-50=50$

Step 6: Calculate the required ratio.

The ratio of female employees in the private sector to those in the government sector is:

$\text{Ratio}=50:50=1:1$