We are given that the daily working power of 2 men and 3 women are equal.
=> 2 Em = 3 Ew
=> Em / Ew = 3/2, where ‘Em’ is the efficiency of 1 man and ‘Ew’ is the efficiency of 1 woman.
Therefore, ratio of efficiency of man and woman = 3 : 2.
If ‘k’ is the constant of proportionality, Em = 3k and Ew = 2k.
Here, we need to apply the formula
∑(M_i E_i) D₁ H₁ / W₁ = ∑(M_j E_j) D₂ H₂ / W₂, where
∑(M_i E_i) = (6 x 3k) + (10 x 2k)
∑(M_j E_j) = (8 x 3k) + (6 x 2k)
D₁ = 15 days
D₂ = Number of days after increasing men and reducing women
H₁ = 6 hours
H₂ = 7 hours
W₁ = 150 km
W₂ = 210 km
 
So, we have
38k x 15 x 6 / 150 = 36k x D₂ x 7 / 210
=> 38k x 6 = 12k x D₂
=> D₂ = 19 days
Therefore, total days required to complete the work = 15 + 19 = 34 days