Question

In a school drill, a number of children are asked to stand in a circle. They are evenly spaced and the 6th child is diametrically opposite the 16th child. How many children are made to stand in the circle?

• A. 16
• B. 20
• C. 22
• D. None of the above

Answer 1

The Correct Option is B

To solve for the total number of children standing in a circle when the 6th child is diametrically opposite the 16th child, we need to determine the total number of children \( n \) in the circle.

In a circle, if one person is diametrically opposite to another, the total number of people between them is half of the circumference. The formula used is:

\[ \text{Position of } B = \text{Position of } A + \frac{n}{2} \mod n \]

Here, the 16th child (B) is opposite the 6th child (A). Thus:

\[ 16 = 6 + \frac{n}{2} \mod n \]

Simplifying, we get:

\[ 16 - 6 = \frac{n}{2} \]

\[ 10 = \frac{n}{2} \]

Multiply both sides by 2 to solve for \( n \):

\[ n = 20 \]

Therefore, the total number of children in the circle is 20.