Re: A company has $X$ employees including few men and few women. The numbe
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31 May 2025, 01:16
A company has:
- Total employees $=X$
- Number of men employees $=Y$
- $Z \%$ of total employees are advocates.
- $P \%$ of women advocates is equal to 40.
Question: What is the number of men advocates?
Options:
(A) $\(\frac{Z X}{100}-\frac{4000}{P}\)$
(B) $\(\frac{Z X}{100}-4000\)$
(C) $\(\frac{Z}{100}-\frac{4000}{P}\)$
(D) $\(\frac{X}{100}-\frac{4000}{P}\)$
(E) $\(Z X-\frac{4000}{P}\)$
Step-by-Step Solution:
1. Define Key Variables:
- Total employees $=X$
- Men employees = Y
- Women employees $=X-Y$
- Total advocates $=Z \%$ of $\(X=\frac{Z}{100} \times X\)$
2. Interpret " $\(P \%\)$ of women advocates is equal to 40 ":
This is ambiguous, but the most logical interpretation is:
" $P$ \% of all women are advocates, and this number equals 40."
So:
$$
\(\begin{gathered}
\frac{P}{100} \times(\text { Number of women })=40 \\
\frac{P}{100} \times(X-Y)=40
\end{gathered}\)
$$
Solve for $X-Y$ :
$$
\(X-Y=\frac{40 \times 100}{P}=\frac{4000}{P}\)
$$
Thus:
$$
\(Y=X-\frac{4000}{P}\)
$$
6. Compare with Options:
We need an expression for men advocates in terms of $X, Z$, and $P$.
From Step 2, we have $\(\frac{4000}{P}=X-Y\)$, but we don't need $Y$ to express men advocates.
The correct expression is:
$$
\text { Men advocates }=\frac{Z X}{100}-40
$$
But none of the options match this exactly.
However, if we reinterpret the problem to mean:
"The number of women advocates is $P \%$ of some quantity, and this equals 40," then:
$$
\text { Women advocates }=\frac{P}{100} \times(\text { some base })=40
$$
But the base is unclear. The most plausible alternate interpretation is: " $P \%$ of women advocates equals 40," which makes no sense because it implies:
$$
\begin{gathered}
\frac{P}{100} \times(\text { women advocates })=40 \\
\text { Women advocates }=\frac{4000}{P}
\end{gathered}
$$
Then:
$$
\text { Men advocates }=\frac{Z X}{100}-\frac{4000}{P}
$$
This matches Option A.
Conclusion:
The most reasonable answer, given the wording, is Option A.
Final Answer: $A$