Select the correct answerIf (a + b) : (b + c) : (c + a) = 7 : 6 : 5 and a + b + c = 27, then what will be the value of 1/a : 1/b : 1/c?Options4 : 3 : 63 : 2 : 43 : 6 : 43 : 4 : 2

The problem can be solved in the following steps:

1. Given that (a + b) : (b + c) : (c + a) = 7 : 6 : 5. This means that a + b = 7x, b + c = 6x, and c + a = 5x for some common ratio x.

2. Also given that a + b + c = 27. We can add the three equations from step 1 to get 2(a + b + c) = 18x. Substituting a + b + c = 27, we get 2*27 = 18x, which gives x = 3.

3. Substituting x = 3 in the equations from step 1, we get a + b = 21, b + c = 18, and c + a = 15.

4. Solving these three equations, we get a = 9, b = 12, and c = 6.

5. The question asks for the values of 1/a : 1/b : 1/c. Substituting the values of a, b, and c, we get 1/9 : 1/12 : 1/6.

6. To simplify, we can multiply each term by the least common multiple of 9, 12, and 6, which is 36. This gives 4 : 3 : 6.

So, the correct answer is 4 : 3 : 6.