Let efficiency of men in group 1 be E1 and that of second group be E2. Ratio of efficiency of men in 1 group to that of 2nd group can be found by using the formula, E1/E2 = Time taken by men in 2nd group to do certain amount of work/Time taken by men in 1 group to do the same amount of work as that of men in 2nd group ⇒ (3 × 1.5) : (2 × 1) ⇒ 4.5 : 2 Now, M1 × D1 × T1 × E1 × W2 = M2 × D2 × T2 × E2 × W1 Where,M1 and M2 = number of men in group 1st and 2nd respectively D1 and D2 = number of days required by the Group 1 and group 2 respectively to complete work T1 and T2 = working hours per day by group 1 and group 2. W1 and W2 = amount of work by group 1 and group2. Since we have to calculate the time taken by group 2 to complete twice the amount of work as that of group 1 W2 = 2 × W1 We had earlier calculated E1/E2 = 4.5/2 Also from the question we can infer that M1 = 20, M2 = 60 T1 = 12, T2 = 4 D1 = 24 and D2 is what we need to find Substituting all the values in eq 1, we can find D2 as follows, ∴ D2 = (20 × 24 × 12 × 4.5 × 2) / (60 × 4 × 2 × 1) = 108 days