If a : (b+c)=1:3 ; c : (a + b) = 5 : 7, then b:(a+c) is equal to?Options2 : 12 : 31 : 21 : 3

The problem is a ratio problem. Here are the steps to solve it:

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

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

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

Step 4: Solve the equation for c, we get c = 15/21b + 5/21c

Step 5: Rearrange the equation, we get 16/21c = 15/21b

Step 6: Simplify the equation, we get c = 15/16b

Step 7: Substitute c from the equation into the first equation, we get a = 1/3(b+(15/16b))

Step 8: Solve the equation for a, we get a = 19/48b

Step 9: Now we have a = 19/48b and c = 15/16b, substitute a and c into the equation b : (a+c), we get b : ((19/48b)+(15/16b))

Step 10: Simplify the equation, we get b : (33/48b)

Step 11: Simplify further, we get b : (33/48)

Step 12: Multiply both sides by 48 to get the final answer, we get b : (a+c) = 48 : 33

So, the answer is 48 : 33.