The duo, aged 15 and 17, was held yesterday from a hotel in the Sindhi Camp area.
The teenagers had befriended the girl from West Bengal on Facebook some months back, and later had planned to leave for the eastern state on her invitation.
On June 16, in the absence of family members, they had left home with the cash, police said.
Finding them untraceable, the family lodged a case of kidnapping following which the police tracked the duo's mobile phones and found the brothers in the hotel.