Judge Nazeer Ahmed Langove and the police official Shafqat Janjua, both escaped unhurt, when their vehicle was targeted with a remote-controlled blast at Quetta's Double Road, senior police official Imran Qureshi said.
The blast, however, killed one person and injured 32 others including two security guards of the Judge, Qureshi said.
"The impact of the explosion smashed glasses of nearby homes and shops in the area and the vehicle was badly damaged," he said.
Quetta is the capital of resource-rich Balochistan province and at the centre of a separatist movement revived since 2004.
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The provincial capital, Quetta, has also been a flashpoint of sectarian violence, mainly targeted at the minority ethnic Hazara community.
Meanwhile, in yet another incident, a government official and his five children were gunned down in Dera Murad Jamali.
Police said that Tehsil Municipal Officer Mehraj Umerani and his five children were gunned down by unidentified men in Haji Sher of Kachhi district.
According to the deputy commissioner of Kuch, Ahmed Ali, the assailants travelling in another car attacked Umerani and his family while they were on their way to Quetta from Dera Murad Jamali on the highway.
"They were a total of 11 people in Umerani's car when it was attacked by the gunmen and three women were also seriously wounded," he added.