The 42-year-old mother and her 10-year-old daughter were found murdered in their Greater Noida flat late Tuesday night.
The boy attacked his mother and sister with a bat and then used a pair of scissors and a pizza cutter to kill them.
The boy had been missing since the incident on Monday night.
According to Noida police sources, the minor, who was on the run after allegedly committing the murder had called his father on Friday morning from an unknown number.
The boy was traced to Dashashwamedh Ghat in Varanasi on Friday, following which police brought him to Noida. "He was quite upset and frustrated and in this rage he committed the heinous crime when his mother and sister were asleep", the note said. "Around 11 am, when his mother and sister were sleeping, he allegedly hit them with a cricket bat and stabbed them with scissors", said SSP of Gautam Budh Nagar Love Kumar.
The police said the teenager, who was weak in studies, was often scolded and beaten up by his mother for playing games on his cell phone for long hours and not paying attention to his studies.
"The boy claimed his mother beat him up when he refused to move to the table to study".
According to the CCTV footage accessed by investigators, Anjali and her children were last seen entering the society around 8 pm that night. Post mortem examination of the two bodies revealed that Anjali had seven injury marks on her head while Kanika had five injury marks on hers. The police have said that the boy took some cash from the house and fled to Chandigarh from where he went to Shimla.
The boy was angry with his mother as she pressured and scolded him for studies, the statement said, adding that his mother scolded him on the day of the incident too, after which he killed them around 11 p.m. He finally took a train to Ranchi and got down at Varanasi. The game was found on other similar electronic devices in the house.