The final solution of HCl should have a molar concentration of 0.25 M. The number of moles of HCl in one liter of the solution should be equal to 0.25.
The process of creating this solution is started with 100 ml of 1 M HCl to which water has to be added. Let the volume of water to be added be X mL. The final solution of HCl would have a volume (0.1 + X/1000) L and the number of moles of HCl present in it is 1/10 = 0.1
This gives: 0.1/(.1 + X/1000) = 0.25
=> 0.1/0.25 = .1 + X/1000
=> 0.4 = 0.1 + X/1000
=> 0.3 = X/1000
=> X = 300 mL
300 milliliter of water should be added to 100 mL of a 1 M solution of HCl to give a 0.25 M solution