Gst application on lease of used car

Dear Madam/Sir,

I am buying a used car using lease from the leasing company tied up with my employer. The car was originally purchased in Bangalore in Jan 2017 by individual after paying the applicable taxes at that time. Now leasing company is going to buy the car from individual and will be going to give me on lease on which individual is ofcourse not going to charge GST. It is a hatchback 1.2ltr car. But the leasing company is charging me the GST @ 29% on the full lease value.

Can you please confirm if the leasing company should charge me the GST on full value or only on the profit they are making and at what rate?

If they charge on the full lease value, is it not the double taxation on the same car? One at the time of original new car purchase and now again when they are leasing me the used one?