Three numbers A, B and C are in the ratio of 12 : 15 : 25. If sum of these numbers is 312, ratio between the difference of B and A and the difference of C and B is ?

Step 1: The first step is to understand the problem. We are given that three numbers A, B, and C are in the ratio 12:15:25. This means that A is 12x, B is 15x, and C is 25x for some number x.

Step 2: We are also given that the sum of these numbers is 312. So, we can write the equation 12x + 15x + 25x = 312.

Step 3: Solving this equation gives us the value of x. The sum of the ratios 12, 15, and 25 is 52. So, we have 52x = 312. Dividing both sides by 52 gives us x = 6.

Step 4: Now that we have the value of x, we can find the actual numbers A, B, and C. Substituting x = 6 into the expressions for A, B, and C gives us A = 72, B = 90, and C = 150.

Step 5: The problem asks for the ratio between the difference of B and A and the difference of C and B. The difference of B and A is 90 - 72 = 18. The difference of C and B is 150 - 90 = 60.

Step 6: Therefore, the ratio between the difference of B and A and the difference of C and B is 18 : 60. This ratio can be simplified by dividing both numbers by their greatest common divisor, which is 6. So, the simplified ratio is 3 : 10.