Ram is in 11th position from left while Shyam is in 9th position from right in the same line. If there are 5 people among them, how many people are there in that line ?

To solve this problem, we need to determine the total number of people in the line using the given positions of Ram and Shyam and the number of people between them.

### Step-by-step Solution:

1. **Understanding the positions**:
   - Ram is in the 11th position from the left.
   - Shyam is in the 9th position from the right.
   - There are 5 people between Ram and Shyam.

2. **Calculating the positions**:
   - Let's denote the total number of people in the line as \(N\).
   - Ram's position from the left is 11th, so there are 10 people to the left of Ram.
   - Shyam's position from the right is 9th, so there are 8 people to the right of Shyam.

3. **Relating Ram's and Shyam's positions**:
   - The people between Ram and Shyam are directly stated to be 5.
   - If there are 5 people between Ram and Shyam, then the number of people from Ram's position to Shyam's position is \(5 + 2 = 7\) (including Ram and Shyam themselves).

4. **Connecting both ends**:
   - We know the positions of Ram and Shyam and the people in between, so the total number of people in the line \(N\) can be found using:
   \[
   N = (\text{Position of Ram from left}) + (\text{Number of people between Ram and Shyam}) + (\text{Position of Shyam from right}) - 1
   \]
   - Plugging in the values:
   \[
   N = 11 + 5 + 9 - 1 = 24
   \]

### Conclusion:
The total number of people in the line is **24**.

Would you like more details on any of the steps, or do you have any other questions?

Here are 5 related questions to consider:
1. If Ram's position changes to 15th from the left, how would that affect the total number of people?
2. How would the answer change if there were 3 people between Ram and Shyam instead of 5?
3. If Shyam's position was instead given as 12th from the right, what would the total number of people be?
4. What if there were no people between Ram and Shyam? How would you find the total?
5. How would you approach this if the total number of people were given and you needed to find the number of people between Ram and Shyam?

**Tip:** When solving problems involving positions in a line, remember to account for both ends of the line and all people in between.

Learn how to calculate the total number of people in a line using given positions of individuals from both ends and the number of people between them. This problem involves positional arithmetic and linear equations, suitable for students in Grades 6-8.

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