Question

3 men and 8 women can do a work in 10 hours.11 men and 13 women can complete the same piece of work in 4 hours. how long will 1 man and 1 woman take to complete the work

Answer 1

1 man and 1 woman will take 2hour and 30 minutes to complete the work....

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Answer 2

Answer:  1 man and 1 woman takes 46.66 hours to complete the work.

Step-by-step explanation:

Since we have given that

3 Men and 8 Women can do a work in = 10 hours

11 Men and 13 Women can do a work in = 4 hours

So, by "Time and work": we get that

$(3m+8w)\times 10=(11m+13w)\times 4\\\\5(3m+8w)=2(11m+13w)\\\\15m+40w=22m+26w\\\\40w-26w=22m-15m\\\\14w=7m\\\\2w=m$

So, we need to find the number of hours will taken by 1 man and 1 woman.

so, our equation becomes

$(3m+8w)\times 10=(m+w)\times x\\\\(6w+8w)\times 10=(2w+w)\times x\ (\because m=2w)\\\\14w\times 10=3w\times x\\\\140w=3w\times x\\\\x=\frac{140w}{3w}\\\\x=46.66\ hours$

Hence, 1 man and 1 woman takes 46.66 hours to complete the work.