I find DI & LR tough while giving mocks due to limited time. Please suggest best or advance level book for the same.
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For your query regarding books, firstly you can get good practice questions in old cat papers and mock CAT by various coaching institutes. For books you can solve Arun Sharma's or Nishit Sinha's for DILR. Also you can practice from a good institutes practice material.
Solving these you should be able to crack one case in around ten minutes on an average.
You can start from the basic level of difficulty and then gradually move to the Advanced Level Of Difficulty. Both these topics LR and DI should be dealt with a different approach:
DI : Comparatively Easy but lengthy and tedious. Mostly, to solve these questions, the knowledge of basic mathematical operations is needed. To ace DI, you need to work on your speed. The faster you do it, the better it is.
LR: Tough and often time consuming. One needs to practice a variety of questions to gain confidence in this section. However there are certain topics like 'Arrangements' which are generally asked every year. So practice all varieties of such commonly asked topics.
To top it up, appear for mocks at regular intervals to track your progress and identify weaker areas.