In a row of boys, A is 20th from left and B is 16th from right, interchange their position, then A becomes 30th from left How many boys are there in the row ?

Options

A. 46
B. 44
C. 45
D. 48

Answer

To solve the problem step-by-step, let's break it down:

1. **Identify A's Position**: A is 20th from the left. This means there are 19 boys to the left of A.

2. **Identify B's Position**: B is 16th from the right. This means there are 15 boys to the right of B.

3. **Interchange Positions**: When A and B interchange their positions, A becomes 30th from the left.

4. **Calculate the Total Number of Boys**:
- After the interchange, A's new position is 30th from the left. This means there are 29 boys to the left of A's new position.
- Since B was originally 16th from the right, we can find the total number of boys in the row using the formula:
\[ \text{Total Boys} = (\text{Position of A from left}) + (\text{Position of B from right}) - 1 \]
- Substituting the values we have:
\[ \text{Total Boys} = 30 + 16 - 1 = 45 \]

5. **Final Answer**: Therefore, the total number of boys in the row is 45.