The ratio of two numbers A and B is 3 : 5. If 6 is added to each of A and B, then the ratio of A and B becomes 21 : 31. The sum of A and B is:Options :39407041

Let's solve this step by step:

Step 1: Let's assume the two numbers A and B are 3x and 5x respectively.

Step 2: According to the problem, if 6 is added to each of A and B, the ratio becomes 21 : 31. So, we can write this as (3x + 6) / (5x + 6) = 21 / 31.

Step 3: Cross multiply to solve for x. This gives us 31*(3x + 6) = 21*(5x + 6).

Step 4: Simplify this to get 93x + 186 = 105x + 126.

Step 5: Rearrange the equation to find the value of x. This gives us 105x - 93x = 186 - 126, which simplifies to 12x = 60.

Step 6: Solve for x by dividing both sides by 12. This gives us x = 60 / 12 = 5.

Step 7: Substitute x = 5 back into the expressions for A and B to find their values. This gives us A = 3x = 35 = 15 and B = 5x = 55 = 25.

Step 8: The sum of A and B is therefore 15 + 25 = 40.

So, the sum of A and B is 40.