Here, we need to apply the formula
∑(Mi Ei) D1 H1 / W1 = ∑(Mj Ej) D2 H2 / W2, where
∑(Mi Ei) = (3 x m) + (4 x w)
∑(Mj Ej) = (13 x m) + (24 x w), where ‘m’ is the efficiency of each man and ‘w’ is the efficiency of each woman
D1 = 10 days
D2 = 2 days
H1 = 12 hours
H2 = 12 hours
W1 = W2 = Work to be doneSo, we have
(3m + 4w) x 10 x 12 = (13m + 24w) x 2 x 12
=> 15m + 20w = 13m + 24w
=> 2m = 4w
=> m = 2w
=> m : w = 2 : 1
Therefore, ratio of efficiency of man and woman = 2 : 1
If the constant of proportionality be ‘k’,
Efficiency of each man = m = 2k
Efficiency of each woman = w = kNow, we re-apply the same formula.
∑(Mi Ei) D1 H1 / W1 = ∑(Mj Ej) D2 H2 / W2, where
∑(Mi Ei) = (3 x m) + (4 x w)
∑(Mj Ej) = (12 x m) + (1 x w)
D1 = 10 days
D2 = Days requires by 12 men and 1 woman
H1 = 12 hours
H2 = 12 hours
W1 = W2 = Work to be doneSo, we have
(3m + 4w) x 10 x 12 = (12m + w) x D2 x 12
=> 30m + 40w = (12m + w) x D2
=> 60k + 40k = (24k + k) x D2
=> 100k = 25k x D2
=> D2 = 4
Therefore, 12 men and 1 woman would require 4 days to complete the work.
