A man was arrested following the incident at 4.10pm yesterday in which the female pedestrians were hit by a red Vauxhall Corsa on Wakefield Road, Streethouse.
The 81-year-old, who was from Pontefract, died at the scene of the accident opposite the Victoria garden centre.
An 89-year-old woman was taken to hospital with serious, life-threatening injuries and was today said to be in a stable condition.
The 21-year-old male driver of the Vauxhall Corsa was arrested on suspicion of causing death by dangerous driving.
He was later released on police bail pending ongoing investigations.
Sgt Carl Quinn, of the Major Collision Enquiry Team, said: “We are appealing for anyone who may have witnessed the collision or saw the involved vehicle beforehand to come forward to assist with our investigation.”
Anyone with information should contact the Major Collision Enquiry Team via 101.