Let’s assume the average age of the new students is x years.

The sum of the ages of the initial 10 students is 10 * 20 = 200 years.

When the 4 new students join, the total number of students becomes 10 + 4 = 14.

The sum of the ages of all 14 students is (10 * 20) + (4 * x) = 200 + 4x years.

The new average age is (200 + 4x) / 14.

According to the problem, the new average age is 20 + 2 = 22 years.

So, we have the equation (200 + 4x) / 14 = 22.

Multiplying both sides of the equation by 14 gives us 200 + 4x = 308.

Subtracting 200 from both sides gives us 4x = 108.

Dividing both sides by 4 gives us x = 27.

Therefore, the average age of the new students is 27 years.