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mrudula
:
6 men and 5 women can do a piece of work done in 6 days same work 3 men and 4 women together work done in 10 days then in how many days does 9 men and 15 women can do
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October 20, 2016 at 8:18am
Little Sky
:
It can be tabulated like this: Men Women Days 6 5 6 3 4 10 9 15 d Let Men be M, Women be W, number of days be D, and the same work they do be J. The equation will look something like this (aM + bW)(D) = J where a is the number of men, b is the number of women Plugging in the values from the table (6M + 5W)(6) = J ...(1) (3M + 4W)(10) = J ...(2) (9M + 15W)(d) = J ...(3) Expanding the equations, 36M + 30W = J ...(1) 30M + 40W = J ...(2) Reversing (2) J = 30M + 40W ...(2) Taking the most recent (1) multiplied by the most recent (2) 36MJ + 30WJ = 30MJ + 40WJ Divided by J throughout 36M + 30W = 30M + 40W Choose M as the subject (in actual fact choosing which as the subject doesn't matter), M = [ieqn]\frac{5}{3}[/ieqn]W We can see that work done by each man is more than the work done by each woman in the same duration. Now, we find J in terms of W Substituting M = [ieqn]\frac{5}{3}[/ieqn]W into (2), 30(5/3)W + 40W = J J = 90W Substituting both J = 90W and M = [ieqn]\frac{5}{3}[/ieqn]W into (3) (9(5/3W) + 15W)(d) = 90W (15W + 15W)(d) = 90W 30Wd = 90W Divided by W throughout, 30d = 90 d = 3
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October 21, 2016 at 1:42am
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