The court granted the relief to Theti and Vaid on the personal surety of Rs 30,000 each and directed them to attend the office of Anti-Corruption Bureau (ACB) every Monday and Thursday.
Theti and Vaid were arrested by ACB last Thursday for allegedly accepting Rs 25,000 bribe from a student seeking admission to class XII in the prestigious college based in Central Mumbai.
In his bail plea, Theti had pleaded innocence.
Meanwhile, arguing for Vaid, her advocate said an accused should not be kept in custody just for the purpose of interrogation and conducting searches.
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The ACB had said they had seized Rs 4.9 lakh in cash from the house of the principal and bank statements, FD documents collectively worth Rs 10.02 lakh from Vaid's house.
Established in late 1930s, the government-aided Khalsa College is among the earliest institutions of higher learning that emerged on the educational landscape of Mumbai.
According to the ACB, the principal had sought money for himself and not as donation to the college when the student concerned came for admission. The student was not eligible for admission as his score was below the cut-off.
According to police, Theti, during the purported conversations, said to the student's family that Rs 25,000 was for his personal usage, no receipt would be given and it would not be considered as donation to the college.