The total numbers of males and females in a town is 70,000. If the number of males is increased by `6%` and that of the females is increased by `4%` , then the total numbers of males and females in the town would become 73520. Whatis the difference between the numberof males and females in the town, in the beginning?

Options

A. 1500
B. 1800
C. 2000
D. 1400

Answer

To solve the problem, we need to find the initial number of males and females in the town and then calculate the difference between them. Let's denote the number of males as \( M \) and the number of females as \( F \).

### Step 1: Set up the equations
We know the following:
1. The total population of the town is 70,000:
\[ M + F = 70000 \]
2. After increasing the number of males by 6% and females by 4%, the new total becomes 73,520:
\[ M + 0.06M + F + 0.04F = 73520 \]
This simplifies to:
\[ 1.06M + 1.04F = 73520 \]

### Step 2: Simplify the second equation
We can rewrite the second equation:
\[ 1.06M + 1.04F = 73520 \]
To eliminate decimals, we can multiply the entire equation by 100:
\[ 106M + 104F = 7352000 \]

### Step 3: Solve the system of equations
Now we have a system of two equations:
1. \( M + F = 70000 \) (Equation 1)
2. \( 106M + 104F = 7352000 \) (Equation 2)

From Equation 1, we can express \( F \) in terms of \( M \):
\[ F = 70000 - M \]

Substituting \( F \) into Equation 2:
\[ 106M + 104(70000 - M) = 7352000 \]
Expanding this:
\[ 106M + 7280000 - 104M = 7352000 \]
Combining like terms:
\[ 2M + 7280000 = 7352000 \]
Subtracting 7280000 from both sides:
\[ 2M = 72000 \]
Dividing by 2:
\[ M = 36000 \]

### Step 4: Find the number of females
Now substituting \( M \) back into Equation 1 to find \( F \):
\[ F = 70000 - 36000 = 34000 \]

### Step 5: Calculate the difference
Now we can find the difference between the number of males and females:
\[ \text{Difference} = M - F = 36000 - 34000 = 2000 \]

### Final Answer
The difference between the number of males and females in the town, in the beginning, is **2000**.

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