The students of a class wrote an exam. `20%` of the boys and `30%` of the girls failed in it. The number of boys who passed in it was 30 more than that of girls. A total of 74 students failed in it. Find the strength of the class.

Options

A. 280
B. 300
C. 320
D. 260

Explanation

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

### Step 1: Define Variables
Let:
- \( b \) = number of boys in the class
- \( g \) = number of girls in the class

### Step 2: Set Up the Equations
According to the problem:
1. **Failed Students**:
- 20% of boys failed: \( 0.2b \)
- 30% of girls failed: \( 0.3g \)
- Total students who failed: \( 0.2b + 0.3g = 74 \)

This gives us our first equation:
\[ 2b + 3g = 740 \quad \text{(Equation 1)} \]

2. **Passed Students**:
- Boys who passed: \( 80\% \) of boys = \( 0.8b \)
- Girls who passed: \( 70\% \) of girls = \( 0.7g \)
- The number of boys who passed is 30 more than the number of girls who passed:
\[ 0.8b = 0.7g + 30 \]

Rearranging gives us our second equation:
\[ 8b - 7g = 300 \quad \text{(Equation 2)} \]

### Step 3: Solve the Equations
Now we have two equations:
1. \( 2b + 3g = 740 \)
2. \( 8b - 7g = 300 \)

To eliminate one variable, we can multiply Equation 1 by 4:
\[ 8b + 12g = 2960 \quad \text{(Equation 3)} \]

### Step 4: Subtract Equation 2 from Equation 3
Now, we subtract Equation 2 from Equation 3:
\[ (8b + 12g) - (8b - 7g) = 2960 - 300 \]
This simplifies to:
\[ 19g = 2660 \]

### Step 5: Solve for \( g \)
Now, divide both sides by 19:
\[ g = \frac{2660}{19} = 140 \]

### Step 6: Substitute \( g \) back to find \( b \)
Now, substitute \( g = 140 \) back into Equation 1:
\[ 2b + 3(140) = 740 \]
This simplifies to:
\[ 2b + 420 = 740 \]
Subtract 420 from both sides:
\[ 2b = 320 \]
Now, divide by 2:
\[ b = 160 \]

### Step 7: Find the Total Strength of the Class
Now, we can find the total strength of the class:
\[ \text{Total strength} = b + g = 160 + 140 = 300 \]

### Final Answer
The strength of the class is **300**.

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