In a row of girls, A is 10th from the left and B is 14th from the right. If…
2022
In a row of girls, A is 10th from the left and B is 14th from the right. If they interchange their positions, A becomes 24th from the left. How many girls are there in the row?
- A.
31
- B.
33
- C.
37
- D.
39
Attempted by 7 students.
Show answer & explanation
Correct answer: C
In row-and-ranking problems, a person's position from the left (L) and from the right (R) in a row of N people are related by L + R - 1 = N. When two people interchange positions, each one's new position from a given end equals the position the other person originally held from that same end.
Let N be the total number of girls in the row. Originally, A is 10th from the left and B is 14th from the right.
Since only A and B interchange positions, A's new position from the left must equal B's original position from the left.
Using the left-right relation for B: B's original position from the left = N - 14 + 1 = N - 13.
A's new position from the left is given as 24, so N - 13 = 24.
Solving this equation gives N = 37.
Cross-check: with N = 37, B's original position from the left works out to 37 - 13 = 24, which is exactly A's stated new position after the interchange, confirming the value is consistent with both given clues.
So the row contains 37 girls in total.