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.

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

If the total number of male employees in Branch T is (X + Y + 2.5)% of the total workforce in Branch S and the total number of female employees in Branch T is one-third of the total male employees in Branches Q and R combined, then what is the total workforce in Branch T?

The correct answer is 620.

To find the total workforce in Branch T, we first determine the values of X and Y from the given table, and then calculate the number of male and female employees in Branch T step-by-step.

Step 1: Find the value of X (Percentage of females in Branch P)
From the table, the total workforce in Branch P is 800.
We are given that the total number of male employees in Branch P is 700.
Therefore, the number of female employees in Branch P is:

$\text{Female employees in P}=800-700=100$

The percentage of female employees in Branch P (X%) is:

$X=\left(\frac{100}{800}\right)\times 100=12.5\%$

Step 2: Find the value of Y (Percentage of females in Branch S)
From the table, the total workforce in Branch Q is 1200, and 60% are female.

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

We are given that the total number of female employees in Branches Q and S together is 945.

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

The total workforce in Branch S is 900. Thus, Y% is:

$Y=\left(\frac{225}{900}\right)\times 100=25\%$

Step 3: Calculate the number of male employees in Branch T
The number of male employees in Branch T is (X + Y + 2.5)% of the total workforce in Branch S.
First, find the percentage:

$X+Y+2.5=12.5+25+2.5=40\%$

Since the total workforce in Branch S is 900:

$\text{Male employees in T}=40\%\text{of}900=\frac{40}{100}\times 900=360$

Step 4: Calculate the number of female employees in Branch T
Female employees in Branch T is one-third of the total male employees in Branches Q and R combined.
• Male employees in Branch Q = (100% - 60%) of 1200 = 40% of 1200 = 480
• Male employees in Branch R = (100% - 40%) of 500 = 60% of 500 = 300

$\text{Total male employees in Q and R combined}=480+300=780$

$\text{Female employees in T}=\frac{1}{3}\times 780=260$

Step 5: Find the total workforce in Branch T

$\text{Total workforce in T}=\text{Male employees in T}+\text{Female employees in T}$

$\text{Total workforce in T}=360+260=620$

Thus, the total workforce in Branch T is 620.