A,B and C can do a piece of work in 10,12 and 15 days respectively. A leaves 5 days before the completion of the work and B leaves 2 days after A. The whole work lasts for

Let total work = L.C.M. (10,12,15) = 60 units

A can complete the work in 10 days, => A's efficiency = $$\frac{60}{10}=6$$ units/day

Similarly, B's efficiency = $$\frac{60}{12}=5$$ units/day

and C's efficiency = $$\frac{60}{15}=4$$ units/day

Let total work is completed in $$x$$ days, => A worked for $$(x-5)$$ days and B for $$(x-3)$$ days

According to ques,

=> $$[6(x-5)]+[5(x-3)]+[4(x)]=60$$

=> $$(6x-30)+(5x-15)+(4x)=60$$

=> $$15x=60+45=105$$

=> $$x=\frac{105}{15}=7$$ days

=> Ans - (A)