The deceased were identified as Md Alamin, 54, headteacher of Bhadra Shimul Dakshinpara Government Primary School in Gabshara union, his wife Sheuli Khatun, 42, his father Md Sohrab Ali, 75, and mother Saleha Begum, 70.
Motiur Rahman, a sub-inspector of Elenga Highway Police Outpost, said the accident took place around 12pm when Md Alamin along with his four family members was heading towards the district town from Bhuapur Upazila.
When they reached Rabna bypass area, a passenger bus rammed into their auto-rickshaw, leaving them injured.
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Later, locals took them to Tangail General Hospital where Sheuli succumbed to her injuries, Motiur said, adding that the other three died while being taken to Dhaka for better treatment, he added.
One family member and the driver survived the crash.