6 men and 10 women were employed to make a road 360 km long. They were able to make 150 kilometres of road in 15 days by working 6 hours a day. After 15 days, two more men were employed and four women were removed. Also, the working hours were increased to 7 hours a day. If the daily working power of 2 men and 3 women are equal, find the total number of days required to complete the work.

**(A)** 19

**(B)** 35

**(C)** 34

**(D)** 50

**Answer:** **(C)** **Explanation:** 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}) D_{1} H_{1} / W_{1} = ∑(M_{j} E_{j}) D_{2} H_{2} / W_{2}**, where

∑(M

_{i}E

_{i}) = (6 x 3k) + (10 x 2k)

∑(M

_{j}E

_{j}) = (8 x 3k) + (6 x 2k)

D

_{1}= 15 days

D

_{2}= Number of days after increasing men and reducing women

H

_{1}= 6 hours

H

_{2}= 7 hours

W

_{1}= 150 km

W

_{2}= 210 km

So, we have

38k x 15 x 6 / 150 = 36k x D

_{2}x 7 / 210

=> 38k x 6 = 12k x D

_{2}

=> D

_{2}= 19 days

Therefore, total days required to complete the work = 15 + 19 = 34 days

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