In a row of boys, A is 7th from the left and B is 12th from the right. If they interchange their positions A becomes 22nd from the left. How many total boys are there in a row?

Question

Accepted Answer

The correct option is 3:
This question is a classic problem in the topic of 'Ranking and Order' or 'Seating Arrangement' in Logical Operations. To find the total number of individuals in a row when a person's position is known from both ends, we use the formula: Total number of persons = (Position from Left + Position from Right) - 1. The key conceptual aspect here is understanding that when positions are interchanged, the new position of one person provides the rank from one side for a specific *seat*, while the original rank of the person who moved to that same seat provides the rank from the other side.

Let’s analyze the positions before the interchange:1.  A is 7th from the Left end.
2.  B is 12th from the Right end.After they interchange their positions, A moves to B’s original seat, and B moves to A’s original seat.
The crucial piece of information is the new position of A: A becomes 22nd from the Left.
Since A is now in B’s original seat, we now know two things about B's original seat:1.  The position of this seat from the Left is 22nd (A's new position).
2.  The position of this seat from the Right is 12th (B's original position).Since we have the rank of the same single position (B's original seat) from both the Left and the Right ends, we can accurately calculate the total number of boys in the row using the formula:
Total Boys = (Position from Left) + (Position from Right) – 1
Total Boys = 22 (A's new position from Left) + 12 (B's original position from Right) - 1
Total Boys = 34 - 1 = 33.
Thus, the total number of boys in the row is 33. This calculation confirms that Option 3, which is 33, is the correct answer.

The incorrect option is 1 (27):
This option would result if a critical piece of information was incorrectly used, perhaps by adding A’s original position (7) and B’s original position (12), and then incorrectly adding A's increase in position (15) instead of the known ranks of the single seat. Alternatively, simply adding A's final position (22) and A's original position (7) yields 29, which is close to 27 if another error was made. Option 27 fails to account for the overlapping positions when the two ranks are combined and is simply too small for the calculated ranks.

The incorrect option is 2 (31):
A result of 31 might arise if a student mistakenly used A's original position (7) instead of B's original position (12) in some form of calculation with A’s new position (22), or if they made an error in the subtraction step. For example, if a student added A’s new position (22) and B’s original position (12) but subtracted 3 instead of 1, they would get 31 (22 + 12 - 3 = 31). However, the standard and correct formula requires subtracting only 1 to prevent double-counting the seat.

The incorrect option is 4 (34):
This option is incorrect because it is the raw sum of the two ranks for the same position (22 + 12). In any problem where the rank of one person/position is taken from both the left and the right sides, the individual in that position is counted twice. The final step of the formula is to subtract 1 to correct for this double-counting. Failing to subtract 1 leads directly to 34, which is one more than the actual total number of boys.