Time & Work level 2 difficulty question
6 men and 8 women can finish construction of a road in 10 days. 26 men and 48 women can finish this in 2 days.
15 men and 20 women are appointed for this task. How many days do they need?
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Ans: Let us consider a man's work in a day as x and a woman's work as y.
6x + 8y = 1/1026x + 48y = 1/2
So, we get
60x + 80y = 1
52x + 96y = 1
60x + 80y = 52x + 96y
=> 60x - 52x = 96y - 80y
=> 8x = 16y
=> x = 2y
6(2y) + 8y = 1/10
=> 12y + 8y = 1/10
=> 20y = 1/10
=> y = 1/200
x = 2y = 2(1/200) = 1/100
So, x = 1/100 and y = 1/200
15 men's one day work = 15/100
20 women's one day work = 20/200
15/100 + 20/200 = 30/200 + 20/200 = 50/200 = 1/4
So, in one day, they can build one fourth of the road.
They need four days to finish the road.
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