Let the three numbers be X, Y and Z.
Z: Y : : 6: 1 $\rightarrow$ Z = 6Y.
Difference between Z and Y is given as 125, i.e, Z - Y = 125.
Let us substitute Z = 6Y here $\rightarrow$ 6Y - Y = 125 $\rightarrow$ 5Y = 125 $\rightarrow$ Y = 25.
Now we can calculate Z = 6Y $\rightarrow$ 6 x 25 = 150.
Difference between Z and X is given as 100, i.e, Z - X = 100 $\rightarrow$ 150 - X = 100 $\rightarrow$ X = 150 - 100 = 50.
Therefore, we can solve this as follows: X+ Y + Z = 50 + 25 + 150 = 225.