What number must be added to each of the numbers 7, 11 and 19 so that the resulting numbers may be in… · ABC26GN3122

Let the required number be $x$. Then, $$\begin{aligned} & (7+x):(11+x)::(11+x):(19+x) \\ & \Rightarrow \frac{7+x}{11+x}=\frac{11+x}{19+x} \Rightarrow(7+x)(19+x)=(11+x)^{2} \\ & \Rightarrow x^{2}+26 x+133=x^{2}+22 x+121 \\ & \Rightarrow 4 x=-12 \Rightarrow x=-3 \end{aligned}$$