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.
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
∑(Mi Ei) D1 H1 / W1 = ∑(Mj Ej) D2 H2 / W2, where
∑(Mi Ei) = (6 x 3k) + (10 x 2k)
∑(Mj Ej) = (8 x 3k) + (6 x 2k)
D1 = 15 days
D2 = Number of days after increasing men and reducing women
H1 = 6 hours
H2 = 7 hours
W1 = 150 km
W2 = 210 km
So, we have
38k x 15 x 6 / 150 = 36k x D2 x 7 / 210
=> 38k x 6 = 12k x D2
=> D2 = 19 days
Therefore, total days required to complete the work = 15 + 19 = 34 days
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