X, Y and Z together can complete a work in 6 days. X as well as Y alone can do the same work in 16 days. In how many days can Z alone complete the same work?

24

 X as well as Y alone can do a work in 16 days.

X one day work = 1/16

Y one day work = 1/16

X, Y, Z can do it together in 6 days

Assume Z takes "z" days to complete the work alone.

Z one day work = 1/z

One day work of X, Y and Z working together = 1/6

⇒1/16 + 1/16 + 1/z = 1/6

1/z = 1/6 - 2/16 = (4-3 )/24

z = 24

The correct answer is Option (3) → 24