There are few males and females in a meeting . If `(3)/(8)` of the people in the meeting are males and there are 90 more females than male how many females are there in the meeting ?

Options

A. 135
B. 200
C. 225
D. None of these

Answer

To solve the problem step by step, let's define the variables and set up the equations based on the information provided.

### Step 1: Define Variables
Let:
- \( m \) = number of males
- \( f \) = number of females

### Step 2: Set Up the Equations
From the problem, we know:
1. \( \frac{3}{8} \) of the total people are males.
2. There are 90 more females than males.

The total number of people in the meeting can be expressed as:
\[ m + f \]

From the first piece of information, we can write:
\[ m = \frac{3}{8}(m + f) \]

From the second piece of information, we can write:
\[ f = m + 90 \]

### Step 3: Substitute the Second Equation into the First
Now, substitute \( f \) from the second equation into the first equation:
\[ m = \frac{3}{8}(m + (m + 90)) \]

### Step 4: Simplify the Equation
Now simplify the equation:
\[ m = \frac{3}{8}(2m + 90) \]

Multiply both sides by 8 to eliminate the fraction:
\[ 8m = 3(2m + 90) \]

Distribute the 3 on the right side:
\[ 8m = 6m + 270 \]

### Step 5: Solve for \( m \)
Now, isolate \( m \):
\[ 8m - 6m = 270 \]
\[ 2m = 270 \]
\[ m = 135 \]

### Step 6: Find the Number of Females
Now, substitute \( m \) back into the equation for \( f \):
\[ f = m + 90 \]
\[ f = 135 + 90 \]
\[ f = 225 \]

### Conclusion
The number of females in the meeting is \( 225 \).

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