According to police, the man, identified as Vikas (22), had demanded Rs 5 lakh threatening to blow up Tagore Modern Public School located in west Delhi's Shalimar Bagh.
Vikas had first threatened Rajni Kholi, principal of the school, on Saturday asking her to hand over the amount or else, he would blow up the school.
"We were given 24 hours to arrange the cash. The principal received a second text message from Vikas next (Sunday) morning, reminding her that 12 hours had already lapsed," said a school official.
"We then realised that the caller must have got the principal's contact details from a board placed outside the school," said a police official.
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Policemen then called on the cell phone number of the accused. "On learning, we were at the other end, he dared us to track him," he added.
During investigation, cops traced the cell phone location to a slum pocket near the school from where he was arrested.