I am going to use the approach by Mr. Kailash Kumar in his article but with modifications.
Since I am a student, I shall take my college campus as a measure of standard. My college holds about 4000 students and there is 1 ATM in my campus. Almost everyone in my campus uses that ATM. That makes it 1 ATM for 4000 people.
Let's try extrapolating my college to the entire country.
There are 1.4 billion people in India.
80% of the country uses a bank.
That makes it One billion One hundred Twenty million people using a bank.
Let's further break down this number to urban and rural.
65% of the Indian population is rural (about 700 million) & about 400 million is urban.
Let's further break this down since it is reasonable to assume that almost everyone in an urban area has an bank account with an active requirement of an ATM service. But, this may not be the case for the rural areas.
In the urban population of about 400 million, let's remove the category of 60+ people (as they may not have an active requirement of an ATM service)
That makes the urban count to about 360 million.
Further, in the category of 0 - 20, it can be reasonable to assume that
the age group of 0 - 15 has no use of an ATM. So, let's remove 30 percent from here.
That makes the urban count to about 240 million.
The rural area is slightly trickier.
Let's discount the age group of 0 - 20 as people with a bank account but with no use of an ATM card.
This reduces the rural count to about 630 million.
Further, lets remove the 60+ category as a group with no use of an ATM.
That reduces the count to about 560 million.
This brings the total to 560 + 240 = 800 million people using ATM.
According to our extrapolation, if there is 1 ATM per 1000 people, there must be about 200,000 ATMs serving 800 million people in India.
The actual number of ATMs stands at about 230,000.