in an IIT class 70% of students are boys and 15% of the students are the member of dramatics club. If 13% of the boys are the member of dramatics club,then what percentage of dramtcid clubs are girls

Let's break down the problem step by step.

### Definitions:
- Let the total number of students in the class be denoted by \( N \).
- 70% of the students are boys, so the number of boys is \( 0.7N \), and the number of girls is \( 0.3N \).
- 15% of the total students are members of the dramatics club, so the total number of dramatics club members is \( 0.15N \).
- 13% of the boys are members of the dramatics club, so the number of boys in the dramatics club is \( 0.13 \times 0.7N = 0.091N \).

### Step-by-Step Solution:
1. The total number of dramatics club members is \( 0.15N \).
2. The number of boys in the dramatics club is \( 0.091N \).
3. The number of girls in the dramatics club can be calculated by subtracting the number of boys from the total number of dramatics club members:
   \[
   \text{Girls in dramatics club} = 0.15N - 0.091N = 0.059N
   \]

4. To find the percentage of dramatics club members who are girls:
   \[
   \text{Percentage of girls in dramatics club} = \left( \frac{0.059N}{0.15N} \right) \times 100 = \frac{0.059}{0.15} \times 100 \approx 39.33\%
   \]

### Final Answer:
Approximately **39.33%** of the members of the dramatics club are girls.

Would you like more details on any part of this calculation?

Here are some related questions to explore:
1. What is the total number of girls in the class if there are 200 students?
2. How would the percentage change if 20% of the boys were in the dramatics club instead of 13%?
3. What is the percentage of boys in the dramatics club relative to the entire class?
4. If the number of boys in the dramatics club increases by 10%, how does that affect the percentage of girls?
5. What is the ratio of boys to girls in the dramatics club?

**Tip:** Always double-check percentages by summing them to ensure they account for the entire group properly.

In an IIT class, 70% of students are boys, and 15% of the students are members of the dramatics club. If 13% of the boys are members of the dramatics club, then what percentage of the dramatics club members are girls?

Solve the problem where 70% of an IIT class are boys, and 15% are members of the dramatics club. This problem involves calculating the percentage of dramatics club members who are girls using basic algebra and percentage concepts. Suitable for Grades 10-12.

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