A can complete 25% of a work in 10 days. B can complete 40% of the same work in 16 days. In how many days will A and B together complete twice the work mentioned above?

A can complete 25% of a work in 10 days.

A can complete the whole work (100%) = $$\frac{10}{25}\times\ 100$$ = 40 days

B can complete 40% of the same work in 16 days.

B can complete the whole work (100%) = $$\frac{16}{40}\times\ 100$$ = 40 days

Let's assume the total work is 40 units.

Efficiency of A = $$\frac{40}{40}$$ = 1 unit/day

Efficiency of B = $$\frac{40}{40}$$ = 1 unit/day

Time is taken by A and B together to complete the same work = $$\frac{40}{1+1}$$

= $$\frac{40}{2}$$

= 20 days

If A and B together complete twice the work mentioned above, then the time taken to do that work will also be twice.

So A and B together complete twice the work mentioned above in $$20\times2$$ = 40 days.