Average Age of New Entrants

Total age of 40 boys = $40 \times 12 = 480$ years.

When 10 new boys join, total students = 50, and new average = $12 + 0.1 = 12.1$ years. Total age of 50 boys = $50 \times 12.1 = 605$ years.

Sum of ages of 10 new boys = $605 - 480 = 125$ years.

Average age of new boys = $\frac{125}{10} = 12.5$ years.