If $$\frac{x}5=\frac{y}6=\frac{z}{11}$$​, then $$\frac{ (x+y+z)}z$$​is equal to:

Correct option is C

Given:

$$\frac{x}{5} = \frac{y}{6} = \frac{z}{11}$$ 

​$$\frac{x + y + z}{z}$$ = ?

Solution: 

Let

$$\frac{x}{5} = \frac{y}{6} = \frac{z}{11} = k$$ 

where k is a constant.

then 

x = 5k, y = 6k, z = 11k

Substituting the expressions for x, y, and z into this expression: 

​$$\frac{x + y + z}{z} = \frac{5k + 6k + 11k}{11k}$$​​

​$$\frac{5k + 6k + 11k}{11k} = \frac{22k}{11k} = 2$$ 

Thus the value of $$\frac{x + y + z}{z}$$ is 2.​