If (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:

Step 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.

Step 2: Adding these three equations, we get 2(a + b + c) = 18x. We know that a + b + c = 27, so substituting this in, we get 2*27 = 18x, which simplifies to x = 3.

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

Step 4: Solving these three equations simultaneously, we find that a = 9, b = 12, and c = 6.

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

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

So, the answer is 4 : 3 : 6.