Explanation

This is a work-rate problem governed by inverse proportion. The total work is fixed: m persons × d days = md person-days to paint the house. With (m + 2) persons, the same md person-days are spread over fewer days, so the time needed is md/(m + 2) days. Options (a) and (b) are ruled out because adding workers must reduce the time, not increase it, and option (c) inverts the fraction. Hence option (d).