Attahullah Khogyani, spokesman for the provincial governor of Nangarhar, said the blasts on November 25 took place in different parts of Jalalabad, the provincial capital.
There was no immediate claim of responsibility for the three bombings in Jalalabad, which has been the scene of a string of deadly attacks by Islamic State (IS) militants.
Khogyani said the first blast was a roadside bomb that exploded outside the house of a local prison official, Abdul Hakim, killing him and a child and wounding six others.
The second explosion hit a fire brigade office, killing three and wounding 21.
Khogyani said the third blast came as people gathered at Hakim's house after the first blast, but there were no reports of casualties.
IS militants have been intensifying their attacks in Afghanistan as Afghan forces, backed by U.S. air strikes, step up attacks against them in eastern Afghanistan, along the porous border with Pakistan.