In class A, total students are `50%` more than total students in class B while both classes have same no. of girls. In class A, there are `70%` boys. Find percentage of girls in class B.

Options

A. A)`20%`
B. B)`30%`
C. C)`50%`
D. D)`45%`

Answer

To solve the problem step by step, we will break down the information given in the question and calculate the required percentage of girls in class B.

### Step 1: Determine the number of students in class B
Let’s assume the total number of students in class B is \( x \).

### Step 2: Calculate the number of students in class A
According to the problem, the total number of students in class A is 50% more than in class B. Therefore, the total number of students in class A can be calculated as:
\[ \text{Total students in class A} = x + 0.5x = 1.5x \]

### Step 3: Assign a value to class B for easier calculations
For simplicity, let’s assume \( x = 100 \) (the total number of students in class B). Then:
\[ \text{Total students in class A} = 1.5 \times 100 = 150 \]

### Step 4: Determine the number of boys in class A
In class A, it is given that 70% of the students are boys. Therefore, the number of boys in class A is:
\[ \text{Number of boys in class A} = 70\% \text{ of } 150 = 0.7 \times 150 = 105 \]

### Step 5: Calculate the number of girls in class A
Since the total number of students in class A is 150 and 70% are boys, the remaining percentage will be girls:
\[ \text{Number of girls in class A} = 150 - 105 = 45 \]

### Step 6: Determine the number of girls in class B
According to the problem, the number of girls in class A is equal to the number of girls in class B. Therefore:
\[ \text{Number of girls in class B} = 45 \]

### Step 7: Calculate the total number of students in class B
We previously assumed that the total number of students in class B is 100. Now we need to find the percentage of girls in class B:
\[ \text{Percentage of girls in class B} = \left(\frac{\text{Number of girls in class B}}{\text{Total students in class B}}\right) \times 100 \]
\[ \text{Percentage of girls in class B} = \left(\frac{45}{100}\right) \times 100 = 45\% \]

### Final Answer
The percentage of girls in class B is **45%**.

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