The most deadly was caused by a car bomb in the mainly Shia Sadr City area.
The same district was hit by a massive truck bomb two days ago that killed more than 60 people and was claimed by Islamic State militants.
Sadr City has been the target of several bomb attacks this year claimed by IS who consider Shia to be heretics.
Saturday's attack targeted a vehicle market in the Habibiya area of Sadr City which had been targeted multiple times in the past, AP news agency said.
Fifteen people were killed and a further 35 injured, officials said.