In an exam 65% children passed in maths and 48% passed in physics and 30% passed in both subjects how many failed in both subjects

Let's solve the problem step by step.

1. **Let the total number of children be \( N \).**

2. **Percentage of children who passed in Mathematics (Maths):**  
   \( 65\% \) of \( N \)  
   So, the number of children who passed in Maths is \( 0.65N \).

3. **Percentage of children who passed in Physics:**  
   \( 48\% \) of \( N \)  
   So, the number of children who passed in Physics is \( 0.48N \).

4. **Percentage of children who passed in both subjects:**  
   \( 30\% \) of \( N \)  
   So, the number of children who passed in both subjects is \( 0.30N \).

5. **To find the percentage of children who passed in at least one subject:**
   - The formula to find this is:
     \[
     \text{Percentage who passed in at least one subject} = \text{Percentage who passed in Maths} + \text{Percentage who passed in Physics} - \text{Percentage who passed in both}
     \]
   - Substituting the given values:
     \[
     = 65\% + 48\% - 30\% = 83\%
     \]
   So, \( 83\% \) of the children passed in at least one subject.

6. **Percentage of children who failed in both subjects:**  
   - If \( 83\% \) passed in at least one subject, then the remaining \( 17\% \) must have failed in both subjects.

Therefore, **17% of the children failed in both subjects.**

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Would you like a detailed explanation or have any further questions?

Here are some related questions:

1. What is the probability that a randomly selected child passed in both subjects?
2. If 200 students took the exam, how many passed in only one subject?
3. How many students passed only in Maths?
4. How many students passed only in Physics?
5. If a child passed in Maths, what is the probability that they also passed in Physics?

**Tip:** When dealing with percentages and overlapping sets, using Venn diagrams can help visualize and solve the problem effectively.

Learn how to calculate the percentage of children who failed in both Maths and Physics given the percentage of children passing in each subject and passing in both subjects. This problem involves percentages, sets, and probability concepts. Suitable for students in Grades 6-8.

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