Select the correct answerIf (a+b) : (b+c) : (c+a) = 5 : 7 : 6 and 2a -3b + 4c = 66 then value of c will be ?

The problem is a combination of ratio and algebraic equations. Here are the steps to solve it:

Step 1: Given that (a+b) : (b+c) : (c+a) = 5 : 7 : 6. This means that a+b, b+c, and c+a are in the ratio 5:7:6 respectively.

Step 2: Let's assume a common ratio k. So, we can write the equations as: a + b = 5k, b + c = 7k, c + a = 6k.

Step 3: Add all three equations, we get: 2a + 2b + 2c = 18k, which simplifies to: a + b + c = 9k.

Step 4: We also know that 2a - 3b + 4c = 66.

Step 5: Multiply the equation from step 3 by 2, we get: 2a + 2b + 2c = 18k.

Step 6: Subtract the equation from step 4 from the equation in step 5, we get: 5b - 2c = 18k - 66.

Step 7: Substitute b + c = 7k (from step 2) into the equation from step 6, we get: 5(7k - c) - 2c = 18k - 66, which simplifies to: 35k - 5c - 2c = 18k - 66, which further simplifies to: 17k = 7c + 66.

Step 8: Solve for c, we get: c = (17k - 66) / 7.

Step 9: Substitute k = (a + b + c) / 9 into the equation from step 8, we get: c = (17(a + b + c) / 9 - 66) / 7.

Step 10: Solve for c, we get: c = 18.

So, the value of c is 18.