Two number are in the ratio 2 : 3. If 2 is subracted from the first and 2 is added to the second, the ratio becomes 1 : 2. The sum of the number is:

30 28 24 10

30

Let the numbers are = 2R & 3R ATQ, \(\frac{2R\;-\;2}{3R\;+\;2}\) = \(\frac{1}{2}\) ⇒ 4R - 4 = 3R + 2 ⇒ 1R = 6 Hence, Sum of numbers = 2R + 3R = 5R = 5 × 6 = 30