For a set of positive numbers \(x_{1},\ x_{2},\ \cdots,\ X_{n}\), the arithmetic mean is given as
\(\text{Arithmetic Mean}=\ \frac{x_{1}\ +\ x_{2}\ +\ \cdots\ +\ x_{n}}{n}\)
Now, set of 12 numbers which includes 10 and 14 has an arithmetic mean of 20.
Let x be the sum of the remaining 10 numbers.
\(AM =\ \frac{x\ +\ 10\ +\ 14}{12} = 20\)

\(\frac{x\ +\ 24}{12}=20\)

\(x=240\ -\ 24=216\) Now, we find the arithmetic mean of the remaining 10 numbers whose sum is 216. \(\therefore\ \frac{x}{10}=\ \frac{216}{10}=21.6\)

\(\frac{x\ +\ 24}{12}=20\)

\(x=240\ -\ 24=216\) Now, we find the arithmetic mean of the remaining 10 numbers whose sum is 216. \(\therefore\ \frac{x}{10}=\ \frac{216}{10}=21.6\)