Question

X, Y and Z together can complete a work in one day. X and Z together can do same work as Y alone do while Y and Z together can do five times as much work as X do alone. Find the time taken by Z to complete the work.​

Answer 1

$\fontsize{18}{10}{\textup{\textbf{Z completes the work in 3 days }}}$

Step-by-step explanation:

Given conditions

a. 1/x+1/y+1/z=1

b. 1/x+1/z=1/y

c. 1/y+1/z=5/x

Adding equation a and b, we get

2/x+2/z=1 or 1/x+1/z=1/2 or 1/x=1/2-1/z...........d

Subtracting a and b

2/y=1

1/y=1/2

Now, from c

1/2+1/z=5(1/2-1/z), using eqn d

1/z+5/z=5/2-1/2

=>6/z=2

=>1/z=1/3

Therefore Z takes 3 days to complete the work alone