Question

The total population of a town is 50,000. The number of males and females increases by 10% and 15% respectively and consequently the population of the town becomes 56,000. What was the number of males in the town?

• A. 20000
• B. 30000
• C. 35000
• D. 40000

Answer 1

The Correct Option is B

The objective is to determine the initial male population of a town with an initial total population of 50,000. The problem provides percentage increases for both male and female populations and the subsequent new total population.

1. Let \( M \) represent the initial number of males and \( F \) represent the initial number of females. The initial total population is given by:
\( M + F = 50000 \) ... (Equation 1)

2. Following the increases, the male population becomes \( M \times (1 + 0.10) = 1.10M \), and the female population becomes \( F \times (1 + 0.15) = 1.15F \).

3. The new total population is stated as 56,000, which can be expressed as:
\( 1.10M + 1.15F = 56000 \) ... (Equation 2)

4. To solve this system of equations, substitute \( F = 50000 - M \) from Equation 1 into Equation 2:

\( 1.10M + 1.15(50000 - M) = 56000 \)
\( 1.10M + 57500 - 1.15M = 56000 \)
\( -0.05M + 57500 = 56000 \)
\( -0.05M = 56000 - 57500 \)
\( -0.05M = -1500 \)
\( M = \frac{-1500}{-0.05} \)
\( M = 30000 \)

Therefore, the initial number of males in the town was 30,000.