$\text{ If the median and range of four numbers }\{\mathrm{x},\mathrm{y},2\mathrm{x}+\mathrm{y},\mathrm{x}-\mathrm{y}\},\text{ where }0<\mathrm{y}<\mathrm{x}<2\mathrm{y}\text{ are }$$10,28\text{ respectively, then the mean of the numbers is }$

$\begin{array}{l}\text{Given that }0<y<x<2y\\ \text{Ascending order of given data is }\\ x-y,y,x,2x+y\\ \text{Range is 28}\\ 2x+y-\left(x-y\right)=28\\ x+2y=28\\ \text{Median: 10}=\frac{x+y}{2}\Rightarrow x+y=20\\ \text{by solving both the above equaitons }y=8,x=12\\ \text{Mean is }\frac{4x+y}{4}=14\end{array}$