4 men of the first group can do (\frac{4}{3}) of the work in (\frac{1}{2}) time as compared to 3 men of the second group who are doing complete work. Find the respective ratio for one day work of 3 men of the first group and 4 men of the second group?

Let T = time for group 2 to complete work. Group 1: 4 men do (4/3) work in T/2 time, so 4 men's 1-day work = (4/3)/(T/2) = 8/(3T). One man of group 1: 2/(3T) per day. Group 2: 3 men do 1 work in T time, so 3 men's 1-day work = 1/T. One man of group 2: 1/(3T) per day. Required ratio: 3 men of group 1 = 3 × 2/(3T) = 2/T; 4 men of group 2 = 4 × 1/(3T) = 4/(3T). Ratio = (2/T) : (4/(3T)) = 3:2.