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}) D_{1} H_{1} / W_{1} = ∑(M_{j} E_{j}) D_{2} H_{2} / W_{2}**, 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

D

_{1}= 10 days

D

_{2}= 2 days

H

_{1}= 12 hours

H

_{2}= 12 hours

W

_{1}= W

_{2}= 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**, where

_{i}E_{i}) D_{1}H_{1}/ W_{1}= ∑(M_{j}E_{j}) D_{2}H_{2}/ W_{2}∑(M

_{i}E

_{i}) = (3 x m) + (4 x w)

∑(M

_{j}E

_{j}) = (12 x m) + (1 x w)

D

_{1}= 10 days

D

_{2}= Days requires by 12 men and 1 woman

H

_{1}= 12 hours

H

_{2}= 12 hours

W

_{1}= W

_{2}= Work to be done

So, we have

(3m + 4w) x 10 x 12 = (12m + w) x D

_{2}x 12

=> 30m + 40w = (12m + w) x D

_{2}

=> 60k + 40k = (24k + k) x D

_{2}

=> 100k = 25k x D

_{2}

=> D

_{2}= 4

Therefore, 12 men and 1 woman would require 4 days to complete the work.

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