Row of girls – Rita is 9th from the right and Monika is 10th from the left. After they swap places, Rita becomes 7th from the right and Monika becomes 18th from the left. How many girls are there in the row?

Introduction / Context:
This is a rank-position puzzle involving left/right counting and the effect of two students (Rita and Monika) swapping places. Normally, after a swap, each person occupies the other's original position. Here, however, the post-swap statements about the new positions create two separate equations for the total number of girls N. If those equations yield different values of N, the data are inconsistent, and the answer must be “Data inadequate.”

Given Data / Assumptions:

• Rita initially is 9th from the right ⇒ Rita's initial left-position = N − 9 + 1 = N − 8.
• Monika initially is 10th from the left.
• They swap places.
• After the swap: Rita is 7th from the right; Monika is 18th from the left.

Concept / Approach:
When two people swap, each takes the other's prior position. Therefore:
• Rita's new position (after swap) = Monika's old position (10th from left).
• Monika's new position (after swap) = Rita's old position (N − 8 from left).
Convert any right-rank to left-rank by left = N − right + 1, or use right = N − left + 1 as needed.

Step-by-Step Solution:

Verification / Alternative check:
Re-derive carefully to rule out arithmetic slips. The conversion formulas and swap logic are standard; repeating the steps yields the same contradiction. Thus, the stem conditions cannot all hold together for a single N.

Why Other Options Are Wrong:

• 25, 26, 27: Any fixed N must satisfy both post-swap conditions. None can satisfy both simultaneously given the equations above (only 26 satisfies the Monika equation; only 16 satisfies the Rita equation; neither satisfies both).
• None of these: “Data inadequate” better captures the contradiction than an unspecified alternative number.

Common Pitfalls:
Assuming one of the post-swap statements is redundant or misapplying the conversion between right- and left-ranks. The correct method is to set up both equations; if they disagree, the data are inconsistent.

Final Answer:
Data inadequate