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Raju is twelfth from the left and Moliit is fifteenth from the right in a row. If we interchange their position, Mobil becomes twentieth from right. How many boys are there in the row?
Ans would be 31.
after interchange Molit was in 12th position from left and 20th position from right
boys remain in left of molit = 11
boys remain in right of molit = 19
total boys = 11+19+1=31
To determine the total number of boys in the row, follow these steps:
1. **Define Positions:**
- Raju is twelfth from the left.
- Moliit is fifteenth from the right.
- After interchanging positions, Moliit becomes twentieth from the right.
2. Calculate Moliit’s Initial Position:
Let the total number of boys in the row be \( N \). After interchanging, Moliit becomes twentieth from the right. Thus, the position of Moliit from the left is:
\[ N - 20 + 1 \]
This is because if Moliit is twentieth from the right, counting from the left gives \( N - 20 + 1 \).
3. Determine Raju’s Position After Interchange:
Moliit’s initial position (from the left) was \( N - 20 + 1 \). If Raju’s initial position from the left is 12, then after the interchange, Moliit would be in Raju’s position. Thus:
\[ N - 20 + 1 = 12 \]
4. Solve for \( N \):
\[ N - 19 = 12 \]
\[ N = 12 + 19 \]
\[ N = 31 \]
So, the total number of boys in the row is 31.
