Select the correct answerIf 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= ?Options9: 4: 128: 5: 1111: 5: 812: 4: 9

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

Step 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.

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

Step 3: We can express x, y, and z in terms of A using the given ratios.

For x, we have A - x = 1k (where k is a constant). So, x = A - 1k.

For y, we have A - y = 7k. So, y = A - 7k.

For z, we have A - z = 4k. So, z = A - 4k.

Step 4: Substitute x, y, and z in the equation 2A = x + y + z.

We get 2A = (A - 1k) + (A - 7k) + (A - 4k).

Solving this, we get 2A = 3A - 12k.

So, A = 12k.

Step 5: Substitute A = 12k in the equations for x, y, and z.

We get x = 12k - 1k = 11k, y = 12k - 7k = 5k, and z = 12k - 4k = 8k.

So, the ratio x:y:z = 11k:5k:8k = 11:5:8.

Therefore, the correct answer is 11:5:8.