Let the number to be added be \(x\). \(\therefore (4 + x):(6 + x) = (6 + x):(10 + x)\) Or, \(\frac{4 + x}{6 + x} = \frac{6 + x}{10 + x}\) Or, \((6 + x)^2 = (4 + x)(10 + x)\) Or, \(36 + 12x + x^2 = 40 + 4x + 10x + x^2\) Or, \(36 + 12x = 40 + 14x\) Or, \(12x - 14x = 40 - 36\) Or, \(-2x = 4\) Or, \(x = -2\) \(\therefore\) If \(-2\) is added to each of 4, 6, and 10, the resulting numbers will be in continued proportion.