Possible... but for the amount of budget, it would make sense to evaluate usage pattern and go for something a bit bigger because your upgrade options would be severely limited.
But if you still want it...
Microtek inverter: 3K (shop around your local Richie street for more options since you're in Chennai)
Microtek Digital Ups Eb 700 Va Inverter: Amazon.in: Home & Kitchen
100AH battery: (7k ~ again, shop around for a better deal, go with tubular)
100AH battery contains 1.2kwh of storage (i.e 1.2 units of power).
Theoretically, it can supply a maximum of 1200 watts for an entire hour. However, real world use would severely limit this on top of converting DC to
AC and you cannot use more than 80% of a lead acid battery, so let's do some maths.
100AH (only 80% capacity usage) - 20% efficiency loss /
C20 discharge rating of a battery.
960 - 192 = 768 / 20 = 38.40 watts continuous operation for 20 hours.
Assuming your fan + led costs 70w, this will work a little over 7 hours depending on the quality of the battery and how it works when its being used beyond its discharge capacity.
Good luck.