Total work always= 100%              

Work done in 1st step  by 300 workers in 21 ( 147 days) = 60% = 60/100   work left =40%

Work washed off by rain = 25% of 60% = 15% =15/100

So the work required to complete by 200 men  = 40% +15% = 55% =  55/100

Now we are equipped well to solve the problem

(i) Algebraic Solution

A men can complete in 1 day = 60/(100*300*147) work               (speed of work)

Speed of 200 men in 1 day =               (200*60)/(100*300*147)

Lets it will take x days to complete the work than 

Speed * time = work done

(200*60)/(100*300*147) * x  = 55/100

so x= (55*100*300*147)/(200*60*100) =  (147*11/8) days = (147*11)/(8*7) days 

                                                                              = (21*11)/8 weeks 

                                                                              = 28 + (7/8)  weeks

(ii) Arithmetic solution

300 workers had worked 147 days to complete the                =                 60/100           work

1 worker worked 1 day to complete                   =                60/(100*300*147) work

200 workers if worked 1 day to complete                       =               (60*200)/(100*300*147) work

                                                                              =               2/(5*147)  work

Now take it as 

200  workers can complete  2/(5*147) work in   = 1 day

200  workers can complete 1 work in                       = (5*147)/2 days

200 workers can complete (55/100) work in            = [(5*147)/2] * (55/100) days

                                                                              =  (147 * 11) / 8 days

                                                                              = (147 * 11) / (8*7) weeks

                                                                              = (21*11/8) weeks

                                                                              =  28 + (7/8) weeks