Question

X, y and z complete a work in 6 days. x for y alone can do the same work in 16 days. in how many days z alone can finish the same work?

Answer 1

x,y,z complete a work in 6 days

Therefore in one day x+y+z do 1/6 part of work, x+y+z=1/6...........(i)

x or y do the same work in 16 days

Therefore x or y do 1/16 part work in one day

Therefore x's one day work= 1/16(x=1/16) and y's one day work =1/16(y=1/16)

Substituting the value of one day's work of x and y in equation (i) we get

x+y+z=1/6

1/16+1/16+z=1/6

z=1/6-1/16-1/16

z=2/48

z=1/24= z's one day work

Therefore z alone can do the whole work in 24 days

Answer 2

In one day:
x+y+z=1 / 6-----1

In one day x's work=1 / 16 ----®
In one day y's work=1 / 16 ---- ©
Sub ® and © in 1
i.e 1/16+1/16+z=1 / 6
2/16+z=1 / 6
z=1 / 24
Therefore 1/24 days z can alone finish same wide