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
∑(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 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.
∑(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 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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