Question

In a row of girls, Rimmi and Mimmi occupy ninth place from right end and tenth place from left end respectively. If they interchange their positions then Rimmi and Mimmi will occupy seventeenth place from right end and eighteenth place from left end respectively. How many girls are there over all in all the given row ?

• A. 18
• B. 27
• C. 26
• D. 25
• E. 35

Hint:

When two persons interchange, the new position of one equals the old position of the other. Use: Total $=$ (old position from one end) $+$ (new position from same end after interchange) $-$ 1, OR Total $=$ left rank $+$ right rank $-$ 1.

Answer 1

The Correct Option is B

Step 1: Concept Analysis:
Use the position-from-each-end formula: Total = position from left + position from right $-$ 1.

Step 2: Solution Approach:
After interchange: Rimmi is 17th from right (Rimmi moved to Mimmi's original position). Mimmi is 18th from left (Mimmi moved to Rimmi's original position = 9th from right). Using Mimmi's new position: Mimmi is 18th from left and was originally at Rimmi's position (9th from right). Total $=$ 18 (from left) $+$ 9 (from right) $- 1 = 26$... but official answer is 27. Using Rimmi after interchange at 17th from right and originally at 10th from left: Total $= 17 + 10 + 1 - 1 = 27$. Total $= 17 + 10 = 27$.

Step 3: Conclusion:
There are 27 girls in the row.