First things first, new generation laptops have come a long way, so almost all laptops from brands like HP, Dell, Sony, Lenovo and even Acer are very good. Choice depends on individual's preference. For example, you can choose Dell for better customer service, HP for better machine, Vaio for better battery life or Lenovo for better durability (life). Performance wise all are more or less same.
Coming to your requirements, you have a lot of options for an Intel Core i3 processor laptop, however, with Core i5, the options are a bit less in your budget. Here is what I would recommend:
1. HP (i5/ 4GB RAM/ 1 GB Graphics) (Anodized Aluminium)
- Priced at Rs. 35.5k on flipkart.
- It has 14 inch screen size and is very portable.
- Does not come with any OS, so you have to afford that cost.
- Has only 1GB graphic card.
2. Lenovo S510p Notebook (4th Gen Ci5/ 4GB/ 500GB/ Free DOS/ 2GB Graph)
- priced at 38k
- matches all your specifications
- Does not come with any OS, so have to afford that cost.
- 3k more than your budget.
Coming to Core i3 processors, the ones that fulfill all your requirements:
1. HP 15-r032TX Notebook (4th Gen Ci3/ 4GB/ 500GB/ Win8.1/ 2GB Graph)
2. Dell Inspiron 14 3442 Notebook (4th Gen Ci3/ 4GB/ 500GB/ Win8.1/ 2GB Graph)
Priced at Rs. 37,000/-
Choose from the above as per you personal preference.
Hope this helps!!