Question

In a class boys stand in a single line. One of the boys is seventeenth in order from both the ends. How many boys are in the class?

• A. \( 34 \)
• B. \( 33 \)
• C. \( 32 \)
• D. \( 27 \)

Hint:

\textbf{Ranking Problems.} In ranking problems where the position of an item is given from both ends of a line, the total number of items can be found by adding the two positions and subtracting 1 (because the item is counted twice).

Answer 1

The Correct Option is B

Let the total number of boys in the class be \( N \). We are given that one boy is seventeenth in order from both the ends. If a boy is seventeenth from the front, it means there are \( 17 - 1 = 16 \) boys standing before him. If the same boy is seventeenth from the back, it means there are \( 17 - 1 = 16 \) boys standing after him. The total number of boys in the class is the number of boys before him, plus the boy himself, plus the number of boys after him. $$ N = (\text{Number of boys before him}) + (\text{The boy himself}) + (\text{Number of boys after him}) $$ $$ N = 16 + 1 + 16 $$ $$ N = 33 $$ Therefore, there are 33 boys in the class. We can also think of this as: Position from the front + Position from the back - 1 = Total number of items. Here, the position from the front is 17, and the position from the back is 17. Total number of boys \( = 17 + 17 - 1 = 34 - 1 = 33 \).