In a town, the present number of employed people is 40,000. If the number of employed men decreases by 4% and the number of employed women increases by 12%, the total employed population becomes 40,480. What is the present number of employed men?

The correct option is 27,000.

Step-by-Step Explanation:

Step 1: Define variables for the population components
Let $M$ be the present number of employed men in the town.
Let $W$ be the present number of employed women in the town.

From the given information, the total present number of employed people is 40,000:

$M+W=\mathrm{40,000}$     — (Equation 1)

Step 2: Express the change in population
The new total employed population becomes 40,480. Therefore, the net increase in the employed population is:

$\text{Net Increase}=\mathrm{40,480}-\mathrm{40,000}=480$

Step 3: Set up the percentage change equation
We are given that:
• The number of employed men decreases by 4%, which is a change of $-0.04M$.
• The number of employed women increases by 12%, which is a change of $+0.12W$.

The net change equals 480, so:

$-0.04M+0.12W=480$     — (Equation 2)

Step 4: Solve the system of equations
From Equation 1, we can express $W$ in terms of $M$:

$W=\mathrm{40,000}-M$

Substitute this expression for $W$ into Equation 2:

$-0.04M+0.12(\mathrm{40,000}-M)=480$

Expand the terms:

$-0.04M+\mathrm{4,800}-0.12M=480$

Combine the terms containing $M$:

$-0.16M+\mathrm{4,800}=480$

Subtract 4,800 from both sides:

$-0.16M=480-\mathrm{4,800}$

$-0.16M=-\mathrm{4,320}$

Divide by -0.16 to find $M$:

$M=\frac{\mathrm{4,320}}{0.16}=\mathrm{27,000}$

Thus, the present number of employed men is 27,000.