X and Y undertook to do a piece of work for Rs 5400. X alone could do this work in 18 days and Y alone could do this work in 24 days. With the assistance of Z they finished the work in 8 days. What is the share (in Rs) of Z ?

Let total work to be done = L.C.M (18,24) = 72 units

X alone could do this work in 18 days, => X's efficiency = $$\frac{72}{18}=4$$ units/day

Similarly, Y's efficiency = $$\frac{72}{24}=3$$ units/day

Let Z's 1 day's work = $$z$$ units/day

According to ques,

=> $$8(4+3+z)=72$$

=> $$7+z=\frac{72}{8}=9$$

=> $$z=9-7=2$$

Now, ratio of efficiencies of X, Y and Z = $$4:3:2$$

=> Z's share in total amount of Rs. 5400 = $$\frac{2}{(4+3+2)}\times5400$$

= $$2\times600=Rs.$$ $$1200$$

=> Ans - (A)