A person X can complete 20% of work in 8 days and another person y can complete 25% of the same work in 6 days. If they work together, in how many days will 40% of the work be completed?

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).