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Question Number 7484 by Obenfo last updated on 31/Aug/16
The ratio of the rate of doing work for  a woman and a man is  2 : 1.   6 women  can complete a work in 20 days. If 2   women and 6 men work together, then  in how many days will they complete   the work?
$$\mathrm{The}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{doing}\:\mathrm{work}\:\mathrm{for} \\ $$$$\mathrm{a}\:\mathrm{woman}\:\mathrm{and}\:\mathrm{a}\:\mathrm{man}\:\mathrm{is}\:\:\mathrm{2}\::\:\mathrm{1}.\:\:\:\mathrm{6}\:\mathrm{women} \\ $$$$\mathrm{can}\:\mathrm{complete}\:\mathrm{a}\:\mathrm{work}\:\mathrm{in}\:\mathrm{20}\:\mathrm{days}.\:\mathrm{If}\:\mathrm{2}\: \\ $$$$\mathrm{women}\:\mathrm{and}\:\mathrm{6}\:\mathrm{men}\:\mathrm{work}\:\mathrm{together},\:\mathrm{then} \\ $$$$\mathrm{in}\:\mathrm{how}\:\mathrm{many}\:\mathrm{days}\:\mathrm{will}\:\mathrm{they}\:\mathrm{complete}\: \\ $$$$\mathrm{the}\:\mathrm{work}? \\ $$
Answered by sandy_suhendra last updated on 31/Aug/16
6 men can complete the work in = (2/1)×20 days = 40 days  in 1 day, 6 men can complete = (1/(40)) of the work  2 women can complete the work in = (6/2)×20 days = 60 days  in 1 day, 2 women can complete = (1/(60)) of the work  in 1 day, 6 men and 2 women can complete = (1/(40))+(1/(60)) = (5/(120 )) = (1/(24)) of the work  so 6 men and 2 women can complete the work in 24 days
$$\mathrm{6}\:{men}\:{can}\:{complete}\:{the}\:{work}\:{in}\:=\:\frac{\mathrm{2}}{\mathrm{1}}×\mathrm{20}\:{days}\:=\:\mathrm{40}\:{days} \\ $$$${in}\:\mathrm{1}\:{day},\:\mathrm{6}\:{men}\:{can}\:{complete}\:=\:\frac{\mathrm{1}}{\mathrm{40}}\:{of}\:{the}\:{work} \\ $$$$\mathrm{2}\:{women}\:{can}\:{complete}\:{the}\:{work}\:{in}\:=\:\frac{\mathrm{6}}{\mathrm{2}}×\mathrm{20}\:{days}\:=\:\mathrm{60}\:{days} \\ $$$${in}\:\mathrm{1}\:{day},\:\mathrm{2}\:{women}\:{can}\:{complete}\:=\:\frac{\mathrm{1}}{\mathrm{60}}\:{of}\:{the}\:{work} \\ $$$${in}\:\mathrm{1}\:{day},\:\mathrm{6}\:{men}\:{and}\:\mathrm{2}\:{women}\:{can}\:{complete}\:=\:\frac{\mathrm{1}}{\mathrm{40}}+\frac{\mathrm{1}}{\mathrm{60}}\:=\:\frac{\mathrm{5}}{\mathrm{120}\:}\:=\:\frac{\mathrm{1}}{\mathrm{24}}\:{of}\:{the}\:{work} \\ $$$${so}\:\mathrm{6}\:{men}\:{and}\:\mathrm{2}\:{women}\:{can}\:{complete}\:{the}\:{work}\:{in}\:\mathrm{24}\:{days} \\ $$

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