X can do a piece of work in 24 days. When he had worked for 4 days, Y joined him. If complete work was finished in 16 days, Y can alone finish that work in:

Let total work to be done = L.C.M. (24,16) = 48 units

X can do a piece of work in 24 days, => X's efficiency = $$\frac{48}{24}=2$$ units/day

Let Y's 1 day work = $$y$$ units/day

Now, X worked for 16 days and Y worked for (16-4) = 12 days

=> $$2(16)+y(12)=48$$

=> $$32+12y=48$$

=> $$12y=48-32=16$$

=> $$y=\frac{16}{12}=\frac{4}{3}$$

$$\therefore$$ Y can finish the work in = $$\frac{48}{\frac{4}{3}}$$

= $$48\times\frac{3}{4}=36$$ days

=> Ans - (A)