Question

x, y and z can do some work in 72 days. x and y together do twice as much as z alone and x and z together can do thrice as much work as y alone. Find the time taken by z alone to do the whole work.

• A. 142 days
• B. 163 days
• C. 184 days
• D. 216 days

Answer 1

The correct option is D 216 days

Given, $(x+y)=2z$
Also, $(x+z)=3y$
$72\times (x+y+z)=1$
Solving for z, we will get:
$72\times (2z+z)=1\Rightarrow 216z=1$
Thus, $z=\frac{1}{216}$
Hence, $z$ will take 216 days to complete the work alone.