F alone can complete a work in 24 days and G alone can complete the same work in 32 days. F and G start the work together but G leaves the work 8 days before the completion of work. In how many days the total work will be completed?
Let total work to be done = L.C.M.(24,32) = 96 units
=> F's efficiency = $$\frac{96}{24}=4$$ units/day and G's efficiency = $$3$$ units/day
Let the work is finished in $$t$$ days, then F alone worked for 8 days, and F and G together worked for $$(t-8)$$ days
According to ques,
=> $$7(t-8)+(4\times8)=96$$
=> $$7t-56+32=96$$
=> $$t=\frac{120}{7}$$ days
=> Ans - (D)
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