A couple and their daughter were found dead at a house at Muradpur in Kadamtali area of the capital on Saturday.
The deceased were identified as Masud Rana, 50, his wife Moushumi Islam and their daughter Jannatul.
Besides, two other members of the family—their granddaughter Marzan Tabbassum and son-in-law Shafiqul Islam are undergoing treatment at Dhaka Medical College and Hospital.
It is suspected that Marzan and Shafiqul fell sick after having toxic food, said police.
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Jamal Uddin, officer-in-charge of Kadamtali Police station, said the three were strangulated to death and their legs and hands were found tied up.
However, police detained Mehzabin Moon, another daughter of the couple, for interrogation.
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Shafiqul, who is undergoing treatment at DMCH, said he along with his wife Mehzabin Moon and daughter Marzan went to his in-law’s house on Friday night.