Calculate Initial Total Age

Find the total age of the 10 men using the initial average of $30$ years.

$T_{initial} = 10 \times 30 = 300$

Determine Remaining Age After Replacement

Subtract the ages of the two men ($24$ and $26$) who left the group from the initial total age.

$T_{remaining} = 300 - 24 - 26 = 250$

Calculate New Total Age

Calculate the new total age of the 10 men based on the new average age of $32$ years.

$T_{new} = 10 \times 32 = 320$

Find Average of Two New Men

Subtract remaining age from new total age to get the sum of new men, then divide by $2$.

$A_{new} = \frac{320 - 250}{2} = \frac{70}{2} = 35$