If x, y, z are three positive numbers such that (A - x): (A - y): (A - z) = 1: 7: 4 and 2A = x+y+z, then x:y:z=

Let say,

$$A-x=k\ ,\ A-y=7k\ and\ A-z=4k.$$

So,$$2A=2\left(k+x\right)\ ,\ 2A=2\left(7k+y\right)\ and\ 2A=2\left(4k+z\right).$$

So,$$x+y+z=2k+2x\ ,\ x+y+z=14k+2y\ and\ \ x+y+z=8k+2z.$$.........................................(1)

or,$$3\left(x+y+z\right)=2\left(x+y+z\right)+2k+14k+8k.\ \ \left(by\ adding\ these\ 3\ equations\right)$$

or,$$x+y+z=24k.$$

put this value in (1) :

$$2x=22k\ or\ x=11k.$$

$$2y=10k\ or\ y=5k.$$

and $$2z=16k\ or\ z=8k.$$

So,$$x:y:z=11:5:8.$$

C is correct choice.