3 men and 5 women can complete a work in 14 days while 6 men can do it in 14 days 4 men and 5 women can complete the work in how many days?
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6 men can complete the work in 14 days means that the work needs 84 man days or a man can do 1/84 of work in a day.
3 men and 5 women can complete the work in 14 days means that the work needs 42 man days and 70 woman days.
42 man days complete 1/84*42=1/2 of work. Remaining 1/2 work needs 70 woman days or a woman can do 1/2÷70=1/2*1/70=1/140 of work in a day.
4 men and 5 women together can do (1/84*4)+(1/140*5)=1/21+1/28=(4+3)/84=7/84=1/12 of work in a day.
Hence the work will be completed in12/1=12 days.
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