Explanation:

Sol. Ans.(a).

Regular method:

X can complete 20% of the work in 8 days. So X can complete the entire work in 40 days. Thus, work done by X in 1 day = 1/40.

Y can complete 25% of the same work in 6 days. So work entire work in 24 days and work done by Y in 1 day = 1/24.

Work done by X and Y in 1 day = 1/40 + 1/24 = 8/120 = 1/15.

That means X and Y can together complete the entire work in 15 days.

So, time taken to finish 40% or 2/5th of the work = 15 × 2/5 = 6 days. So the correct option is (a).

Alternative method:

X can complete 20% of the work in 8 days so he will complete 40% of the work in 16 days or 48/3 days.

Y can complete 25% of the work in 6 days so he will complete 40% of the work in 6×40/25 = 48/5 days.

If both work together, the work will be completed in 1/(5/48+3/48)=1/(8/48)=1/(1/6)=6 days