Select the correct answerIf a : (b+c)=1:3 ; c : (a + b) = 5 : 7, then b:(a+c) is equal to?Options2 : 11 : 21 : 32 : 3

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

Step 1: From the first equation, we can write a = 3(b+c)

Step 2: From the second equation, we can write c = 7/5(a+b)

Step 3: Substitute a from equation 1 into equation 2, we get c = 7/5(3(b+c)+b) = 21/5(b+c) + 7/5b

Step 4: Simplify the equation, we get c = 21/5b + 21/5c + 7/5b

Step 5: Rearrange the equation, we get 4/5c = 28/5b

Step 6: Simplify the equation, we get c = 7b

Step 7: Substitute c = 7b into equation 1, we get a = 3(b+7b) = 24b

Step 8: Now we have a = 24b and c = 7b, so b : (a+c) = b : (24b + 7b) = b : 31b = 1 : 31

So, the correct answer is 1 : 31.