If a, b, c are three positive integers such that a and b are in the ratio 3 : 4 while b and c are in the ratio

Question

If a, b, c are three positive integers such that a and b are in the ratio 3 : 4 while b and c are in the ratio 2:1, then which one of the following is a possible value of (a + b + c)?

Accepted Answer

207. a : b = 3:4 and b : c = 2:1 => a:b:c = 3:4:2 => a = 3x, b = 4x , c = 2x => a + b + c = 9x => a + b + c is a multiple of 9. From the given options only, option C is a multiple of 9