The number of boys and girls who appeared in an exam were in the ratio of 9:7. The number of boys & girls passing exam were in the ratio 3:2. If 60% of girls passed in exam, find the percentage of boys passed in exam.

Options

A. 0.64
B. 0.72
C. 0.7
D. 0.8

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Ratios
The number of boys and girls who appeared in the exam is given in the ratio of 9:7. This means for every 9 boys, there are 7 girls.

### Step 2: Assign Variables
Let the number of boys be \( 9x \) and the number of girls be \( 7x \), where \( x \) is a common multiplier.

### Step 3: Calculate the Total Number of Students
The total number of students who appeared for the exam is:
\[ 9x + 7x = 16x \]

### Step 4: Determine the Number of Girls Who Passed
It is given that 60% of the girls passed the exam. Therefore, the number of girls who passed is:
\[ \text{Girls Passed} = 60\% \text{ of } 7x = \frac{60}{100} \times 7x = 4.2x \]

### Step 5: Use the Passing Ratio
The ratio of boys passing to girls passing is given as 3:2. Let the number of boys who passed be \( 3y \) and the number of girls who passed be \( 2y \).

### Step 6: Set Up the Equation for Girls Passing
From the previous step, we know that:
\[ 2y = 4.2x \]
Solving for \( y \):
\[ y = \frac{4.2x}{2} = 2.1x \]

### Step 7: Find the Number of Boys Who Passed
Using the value of \( y \):
\[ \text{Boys Passed} = 3y = 3 \times 2.1x = 6.3x \]

### Step 8: Calculate the Total Number of Boys
From Step 2, we know the total number of boys is \( 9x \).

### Step 9: Calculate the Percentage of Boys Who Passed
Now, we can calculate the percentage of boys who passed the exam:
\[ \text{Percentage of Boys Passed} = \left( \frac{\text{Boys Passed}}{\text{Total Boys}} \right) \times 100 = \left( \frac{6.3x}{9x} \right) \times 100 \]
The \( x \) cancels out:
\[ = \left( \frac{6.3}{9} \right) \times 100 = 70\% \]

### Final Answer
The percentage of boys who passed the exam is **70%**.

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