QA – Placement Quizzes | Work and Wages | Question 9

3 men and 4 women can complete a work in 10 days by working 12 hours a day. 13 men and 24 women can do the same work by working same hours a day in 2 days. How much time would 12 men and 1 women working same hours a day will take to complete the whole work?
(A) 4
(B) 6
(C) 8
(D) 10

Answer: (A)
Explanation: 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) = (3 x m) + (4 x w)
∑(M_j E_j) = (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 done

So, 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 = k

Now, we re-apply the same formula.
∑(M_i E_i) D₁ H₁ / W₁ = ∑(M_j E_j) D₂ H₂ / W₂, where
∑(M_i E_i) = (3 x m) + (4 x w)
∑(M_j E_j) = (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 done

So, 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.
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