If A : B = 2 : 3 and B : C = 3 : 7, then A + B : B + C : C + A is

To solve this problem, we first need to find the ratio of A : B : C.

Given that A : B = 2 : 3 and B : C = 3 : 7, we can equate the value of B in both ratios to find the ratio of A : B : C.

To do this, we multiply the first ratio by 3 and the second ratio by 3, which gives us A : B = 6 : 9 and B : C = 9 : 21.

So, A : B : C = 6 : 9 : 21.

Next, we find the ratio A + B : B + C : C + A.

A + B = 6 + 9 = 15, B + C = 9 + 21 = 30, C + A = 21 + 6 = 27.

So, A + B : B + C : C + A = 15 : 30 : 27.

This ratio can be simplified by dividing each term by 3, which gives us 5 : 10 : 9.

Further simplifying by dividing each term by 5, we get the final ratio as 1 : 2 : 1.8.