A woman and a boy and a man can do a work in 3 days together .if man alone can do it in 6 days and a boy alone complete it in 18 days ,in how many days a woman alone can complete it ?aand b completea work in 12 and 18 days respectively .theystarted togetherbut after 2 days a had to leave.in how much time b will complete the remained work?
Answers
Woman,man and boy do a work in 3 days working together; therefore ,
woman+man+boy one day's work =1/3; w+m+b=1/3....(i)
man alone does in 6 days; therefore man's one day work = 1/6; m=1/6...(ii)
boy alone does in 18 days; therefore boy's one day work = 1/18; b=1/18...(ii)
Substituting the values of m and b in equation (i) we get,
w+1/6+1/18=1/3
w=1/3-1/6-1/18
w=1/9 (this is woman's one day's work)
Therefore woman working alone can do the whole work in 9 days.
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a can do a work alone in 12 days; therefore a does 1/12th part of work in one day; a=1/12....(i)
b can do a work alone in 18 days; therefore a does 1/18th part of work in one day; b=1/18....(ii)
Therefore in 2 days a+b complete 2/12+2/18 part of work; a+b=2/12+2/18=5/18;
a+b=5/18....(iii); therefore work left to be done = 1-5/18=13/18
b has to complete 13/18 of work (remaining work)
b does whole work in 18 days
therefore b does 13/18 part of work in 13/18*18= 13 days.
Hope this is clear and helpful . Pl comment for clarifications!