If a : (b+c)=1:3 ; c : (a + b) = 5 : 7, then b:(a+c) is equal to?Options1 : 32 : 32 : 11 : 2

The problem is a ratio problem involving three variables a, b, and c. Here are the steps to solve it:

Step 1: From the first equation a : (b+c) = 1:3, we can write it as a/(b+c) = 1/3. Let's call this equation (1).

Step 2: From the second equation c : (a + b) = 5 : 7, we can write it as c/(a+b) = 5/7. Let's call this equation (2).

Step 3: We need to find the value of b:(a+c). But from the given equations, we don't have a direct way to find this. So, we need to manipulate the equations a bit.

Step 4: Multiply equation (1) by 5 and equation (2) by 3. We get 5a = b+c and 3c = a+b.

Step 5: Subtract the second equation from the first to get 5a - 3c = b - c. Simplify to get 2a = 2c + b.

Step 6: Divide both sides by 2 to get a = c + b/2.

Step 7: Substitute a = c + b/2 into equation (1) to get c + b/2 = b+c. Simplify to get b = 2c.

Step 8: Substitute b = 2c into equation (1) to get a = 3c.

Step 9: Now we have a = 3c and b = 2c. So, b:(a+c) = 2c : (3c + 2c) = 2c : 5c = 2 : 5.

So, the answer is 2 : 5.