In an examination out of 240 students 70% boys and 80% girls passed. How many girls appeared in the examination, if total pass percentage was 74%?

To solve this problem, let's break it down step by step.

### Step 1: Define the variables
- Let \( x \) be the number of boys who appeared for the examination.
- Let \( y \) be the number of girls who appeared for the examination.

### Step 2: Set up equations based on the given data
- Total students: \( x + y = 240 \).
- Number of boys who passed: \( 0.7x \).
- Number of girls who passed: \( 0.8y \).
- Total number of students who passed: \( 0.74 \times 240 = 177.6 \).

### Step 3: Create an equation for the total pass percentage
The total number of students who passed is the sum of boys who passed and girls who passed:
\[
0.7x + 0.8y = 177.6
\]

### Step 4: Solve the system of equations
We now have two equations:
1. \( x + y = 240 \)
2. \( 0.7x + 0.8y = 177.6 \)

Let's solve these equations simultaneously.

#### Substituting \( y = 240 - x \) into the second equation:
\[
0.7x + 0.8(240 - x) = 177.6
\]

#### Simplifying the equation:
\[
0.7x + 192 - 0.8x = 177.6
\]
\[
-0.1x + 192 = 177.6
\]
\[
-0.1x = 177.6 - 192
\]
\[
-0.1x = -14.4
\]
\[
x = \frac{-14.4}{-0.1} = 144
\]

So, the number of boys who appeared is \( x = 144 \).

#### Find the number of girls:
\[
y = 240 - 144 = 96
\]

### Conclusion:
The number of girls who appeared in the examination is **96**.

Would you like further details or have any questions?

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Here are some related questions:
1. What would be the number of girls who passed the exam?
2. If the pass percentage for girls was 85%, how would that affect the total pass percentage?
3. How many boys did not pass the exam?
4. What is the total number of students who failed the exam?
5. What would happen if the total number of students was 300 instead of 240?

**Tip:** When solving problems with percentages and totals, setting up clear equations based on the variables is crucial for finding accurate solutions.

Explore how to solve a percentage problem involving boys and girls in an examination. Learn step-by-step how to calculate the number of girls who appeared in the examination based on given pass percentages. Suitable for Grades 9-12.

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