Ratio Proportion

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)?

  1. 201
  2. 205
  3. 207
  4. 210

Answer

a : b = 3 : 4 and b : c = 2 : 1

Multiplying the second ratio by 2, you get

a : b = 3 : 4 and b : c = 4 : 2

Therefore, a : b : c = 3 : 4 : 2

⇒ a = 3k, b = 4k, c = 2k

Since a, b and c are positive integers, their sum should be 9k, a positive integer.

From the options, only choice C, which is 207, is a multiple of 9.

The correct option is C.