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= ?Options8: 5: 1111: 5: 812: 4: 99: 4: 12

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

Given that (A - x): (A - y): (A - z) = 1: 7: 4 and 2A = x+y+z.

Let's assume A - x = 1k, A - y = 7k, and A - z = 4k for some constant k.

Then, we can write the equations as follows:

A = x + 1k, A = y + 7k, A = z + 4k.

Adding these three equations, we get 3A = x + y + z + 12k.

But we know that 2A = x + y + z, so we can substitute this into the equation to get 3A = 2A + 12k.

Solving for A, we get A = 12k.

Substitute A = 12k into the equations A = x + 1k, A = y + 7k, and A = z + 4k, we get:

x = 11k, y = 5k, z = 8k.

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

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