X can do a piece of work in 8 days, Y can do it in 10 days and Z can do it in 20 days. In how many days can X, Y and Z together complete the work?

First, we need to find the work done by X, Y, and Z in one day.

X's one day work = 1/8 Y's one day work = 1/10 Z's one day work = 1/20

Now, let's add these to find the work done by all three in one day.

Total one day work = X's one day work + Y's one day work + Z's one day work Total one day work = 1/8 + 1/10 + 1/20

To add these fractions, we need to find a common denominator. The least common multiple of 8, 10, and 20 is 40. So, let's convert each fraction to have this common denominator:

X's one day work = 5/40 Y's one day work = 4/40 Z's one day work = 2/40

Now, add these fractions:

Total one day work = 5/40 + 4/40 + 2/40 = 11/40

This means that together, X, Y, and Z can complete 11/40 of the work in one day. To find out how many days they would take to complete the whole work, we divide the total work (1) by the work they can do in one day (11/40):

Total days to complete the work = 1 / (11/40) = 40/11 ≈ 3.64 days

So, X, Y, and Z together can complete the work in approximately 3.64 days.