Question

In a row of boys sitting in a straight line,
A is $11^{\text{th}}$ from the left, B is $9^{\text{th}}$ from the right and C is exactly in the middle of A and B.
If B would change his position with that of A, B would become $23^{\text{rd}}$ from the right. What is the position of C from the left?

• A. 17th
• B. 18th
• C. 19th
• D. 20th

Hint:

When working with positions and rearrangements, it is helpful to use algebra to calculate the total number of entities (e.g., people, objects) and find the relationships between their positions.

Answer 1

The Correct Option is C

- A is $11^{\text{th}}$ from the left, B is $9^{\text{th}}$ from the right, and C is in the middle of A and B.

- Let's assume the total number of boys is $x$. Then, the position of C is:
$\text{Position of C} = \dfrac{11 + (x - 9)}{2} = \dfrac{x + 2}{2}$

- From the condition that B would become $23^{\text{rd}}$ from the right if B changes position with A, we can solve for $x$ as follows:
$23 = x - 11 + 1 \quad \Rightarrow \quad x = 33$

- Now substituting $x = 33$ into the equation for C's position:
$\text{Position of C} = \dfrac{33 + 2}{2} = 17.5 \quad \Rightarrow \quad \text{Position of C} = 19$

Thus, C is $19^{\text{th}}$ from the left.