In a row of 63 students facing North, Ashna is 22nd from the right end. If…

Concept

In a single line of n people who all face the same way, one person's rank counted from the left end and the same person's rank counted from the right end always add up to n + 1.

So a right-end rank converts to a left-end rank as: rank from left = n − (rank from right) + 1. And shifting a person k places towards the left end lowers that person's rank-from-left by exactly k.

Application

1. The row holds n = 63 students, and Ashna is 22nd from the right end.

2. Convert Ashna's rank to a left-end rank: 63 − 22 + 1 = 42, so Ashna stands 42nd from the left.

3. Sona stands 28 places to the left of Ashna, so subtract that shift: 42 − 28 = 14.

4. Sona therefore stands 14th from the left end of the row.

Cross-check

Do the same journey counting from the right instead. Moving 28 places to the left of Ashna moves Sona 28 places further away from the right end, so Sona is 22 + 28 = 50th from the right. Converting that back gives 63 − 50 + 1 = 14th from the left, and the two independent routes agree.

Watch out

The phrase "facing North" only fixes that every student faces the same way, so left and right mean the same thing for the row and for each student; it changes none of the arithmetic. The usual slip is writing 63 − 22 = 41 for Ashna's left-end rank, which forgets that Ashna herself is counted in both ranks and drags the final position one place too low.