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= ?Options12: 4: 99: 4: 128: 5: 1111: 5: 8

To solve this problem, we need to use the concept of ratios and proportions. Here are the steps:

1. We are given that (A - x): (A - y): (A - z) = 1: 7: 4. This means that A - x, A - y, and A - z are in the ratio 1:7:4.

2. We are also given that 2A = x + y + z.

3. We can express x, y, and z in terms of A using the given ratios. From the first ratio, we can write: x = A - 1k (where k is a constant representing the common difference in the ratio), y = A - 7k, z = A - 4k.

4. Substituting these values into the second equation gives: 2A = (A - 1k) + (A - 7k) + (A - 4k) Simplifying this gives: 2A = 3A - 12k Solving for A gives: A = 12k.

5. Substituting A = 12k into the equations for x, y, and z gives: x = 12k - 1k = 11k, y = 12k - 7k = 5k, z = 12k - 4k = 8k.

6. Therefore, the ratio x:y:z is 11k:5k:8k, which simplifies to 11:5:8.

So, the correct option is 11:5:8.