In a row of boys, Sandeep is eleventh from the right and Deepak is also…
2017
In a row of boys, Sandeep is eleventh from the right and Deepak is also eleventh from the left. When Sandeep and Deepak interchange their positions, Deepak become seventeenth from the left. How many boys are there in the row?
- A.
25
- B.
30
- C.
27
- D.
26
Show answer & explanation
Correct answer: C
Concept
In any single row of a fixed number of items, for any one position the count from the left plus the count from the right always equals the total number of items plus one: (rank from left) + (rank from right) = Total + 1. A useful corollary: when two people swap seats, each one simply inherits the other's exact seat, so the new rank of the mover equals the rank of the seat it moved into.
Application
Sandeep sits at the seat that is 11th from the right end of the row.
When Sandeep and Deepak swap, Deepak moves into Sandeep's seat, so Deepak now occupies the seat that is 11th from the right.
We are told that in this new seat Deepak is 17th from the left. So this one seat is at the same time 17th from the left and 11th from the right.
Apply the identity to that single seat: Total + 1 = (rank from left) + (rank from right) = 17 + 11 = 28.
Therefore Total = 28 - 1 = 27 boys.
Cross-check
Independent check via Deepak's shift: Deepak started 11th from the left and ended 17th from the left, a move of 6 seats to the right. Sandeep was 11th from the right, i.e. (27 - 11 + 1) = 17th from the left, which is exactly where Deepak landed - and 17 is indeed 6 more than 11. The two methods agree, confirming a row of 27.