it takes six days for two men and three women working together to complete a work. three men would do the same work five days sooner than nine women. how many times does the output of a man exceed that of a woman?
Answers
Given:
It takes six days for two men and three women working together to complete a work. three men would do the same work five days sooner than nine women.
To find:
How many times does the output of a man exceed that of a woman?
Solution:
From given, let us consider the followings:
If 9 women, 1-day work = 1/x ---(1)
So 3 men, 1 day work = 1/(x-5) ---(2)
Also given 3 women and 2 men 1-day work = 1/6 ---(3)
From (1), we have,
3 women 1-day work = 1/3x
From (2), we have,
2 men 1 day work = 2/[3(x-5)]
Equation (3) can be represented as, 1/3x + 2/[3(x-5)]= 1/6
Solving the equation, we get, x = 10
So 1 woman 1 day work=1/(9 × 10)= 1/90 and
1 man 1 day work=1/3(10-5)= 1/15
The output of men exceeds that of a women = (1/15)/(1/90)= 6 times
Therefore, 6 times the output of a man exceeds that of a woman