X and Y can complete a piece of work in 16 days, Y and Z can do the same piece of work in 24 days. X, Y and Z together can do it in 12 days. How much time will X and Z take to finish it?

Correct option is B

Given: 

Time taken by 

​$$x$$ and $$y$$ = 16 days

​$$y$$ and $$z$$ = 24 days

$$x,y$$ and $$z$$ = 12 days 

Solution:

The work rate

​$$x+y = \dfrac{1}{16}$$ ----- (1)

$$y+z=\dfrac{1}{24}$$  ----- (2)

$$x+y+z=\dfrac{1}{12}$$  ----- (3)

Substitute equation (1) in (3)

​$$\dfrac{1}{16}+z=\dfrac{1}{12}$$

$$z=\dfrac{1}{12}-\dfrac{1}{16}$$

$$z=\dfrac{4}{192}=\dfrac{1}{48}$$

Substitute equation (2) in (3) 

​$$x+\dfrac{1}{24}=\dfrac{1}{12}$$

$$x=\dfrac{1}{12}-\dfrac{1}{24}$$

$$x=\dfrac{12}{288}=\dfrac{1}{24}$$

the combined work rate of x and z

$$x+z=\dfrac{1}{24}+\dfrac{1}{48}=\dfrac{3}{48}=\dfrac{1}{16}$$  

Therefore, time taken by $$x$$ and$$z$$ is 16 days