A sports club has 130 memebrs. An increase of 10% in the number of men and 20% in the number of ladies brought up the menbership to 148. How many men and ladies were there originally?

Options

A. 90 men, 40 women
B. 80 men, 50 women
C. 60 men, 70 women
D. 50 men, 80 women

Answer

To solve the problem step by step, we will define the variables and set up the equations based on the information given.

### Step 1: Define the variables
Let:
- \( m \) = number of men originally
- \( l \) = number of ladies originally

### Step 2: Set up the equations
From the problem, we know that:
1. The total number of members is 130:
\[ m + l = 130 \quad \text{(Equation 1)} \]

2. After a 10% increase in the number of men and a 20% increase in the number of ladies, the total membership becomes 148:
- The new number of men = \( m + 0.1m = 1.1m \)
- The new number of ladies = \( l + 0.2l = 1.2l \)

Therefore, we can write the second equation as:
\[ 1.1m + 1.2l = 148 \quad \text{(Equation 2)} \]

### Step 3: Solve the equations
We have the following system of equations:
1. \( m + l = 130 \) (Equation 1)
2. \( 1.1m + 1.2l = 148 \) (Equation 2)

#### Step 3.1: Rearranging Equation 1
From Equation 1, we can express \( l \) in terms of \( m \):
\[ l = 130 - m \]

#### Step 3.2: Substitute \( l \) in Equation 2
Now, substitute \( l \) in Equation 2:
\[ 1.1m + 1.2(130 - m) = 148 \]

#### Step 3.3: Simplify the equation
Expanding the equation:
\[ 1.1m + 156 - 1.2m = 148 \]
Combine like terms:
\[ -0.1m + 156 = 148 \]

#### Step 3.4: Solve for \( m \)
Subtract 156 from both sides:
\[ -0.1m = 148 - 156 \]
\[ -0.1m = -8 \]
Now, divide by -0.1:
\[ m = \frac{-8}{-0.1} = 80 \]

### Step 4: Find \( l \)
Now that we have \( m \), we can find \( l \):
\[ l = 130 - m = 130 - 80 = 50 \]

### Conclusion
Thus, the original number of men and ladies in the sports club is:
- Men: \( 80 \)
- Ladies: \( 50 \)

### Summary
- Originally, there were **80 men** and **50 ladies** in the club.