Aman and Raman together complete a piece of work in 30 days, Raman and Manan can complete the same work in 36 days and Manan and Aman can complete the same work in 45 days. All of the three working together can complete the work in how many days? ?->(Show Answer!)

1. Aman and Raman together complete a piece of work in 30 days, Raman and Manan can complete the same work in 36 days and Manan and Aman can complete the same work in 45 days. All of the three working together can complete the work in how many days?

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By: anil on 05 May 2019 02.26 am

Let total work to be done = L.C.M. (30,36,45) = 180 units Let efficiency of Aman, Raman and Manan be $$x,y$$ and $$z$$ units/day respectively. Aman and Raman together complete a piece of work in 30 days, => $$(x+y)=frac{180}{30}=6$$ units/day
Similarly, $$(y+z)=5$$ and $$(z+x)=4$$ Adding all the equations, we get : $$2(x+y+z)=6+5+4=15$$ => $$(x+y+z)=frac{15}{2}=7.5$$ $$ herefore$$ Time taken by all of them working together = $$frac{180}{7.5}=24$$ days => Ans - (C)

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