For difference of around 3-5k, you were looking for AMD A4 processor against 5th generation i3. I would still suggest, stick to earlier models suggested.
With acer you would be compromising with build quality compared to asus ..i would still suggest to go with asus
this is the cheapest asus I could find 25.8k (you could find some ebay codes on here get 1k-2k discount and it would be best deal overall)
To get an all in one package in intel you have to increase your budget a bit !! as you need a Low to mid range multimedia laptop for (web surfing/office apps/Casual Gaming) it got to have a minimum of 64 bit GPU .. Unless you are just playing counter strike and some older games on it , as intel HD graphics would be sufficient ! Plus you are also looking for a genuine windows
HP 15-AF114AU
Price : Rs 25,990
Best laptops under Rs 25,000 HP 15-af114AU
Features:
Processor: AMD A8-7410 2.2GHz quad core
RAM: 4GB DDR3
Hard Disk: 1TB -5400 RPM Hard Disk
Display: 15.6 inch 1366 x 768 Pixels display
Graphics card: Radeon R5
OS: Windows 10
ASUS A555LA-XX2384D
25,890RS
CORE I3-5TH GENERATION
intel HD graphics
2 years Warranty
Asus X555YA-XX067D
25,899 RS
Processor : AMD A6 7310
Screen : 39.62cm (15.6)
Memory (RAM) : 8 GB
Hard Disk Capacity : 500GB HDD
Graphics : AMD Radeon™ R4 Graphics Built-in A6-7310
Operating System : Windows 10 HOME (64bit)