What I did was I subtracted (8400+9680) from 25088, which is principle for third year using CI formula. They have subtracted the amount which was paid at the year end to get Principle for next year. Is it a valid concept of C.I. and I missed something?

Hi,
What you have missed is "the time value of money". Rs. 8400 paid at the end of the first year is different from Rs. 8400 paid at the end of the third year. The most fundamental thing about comparing money is that everything must be brought to the same time frame.

If you wish to compare by the beginning of 3 years, Rs. 20000 would have amounted to 25088 by the beginning of three years.

8400 is paid at the end of the first year. => 8400 will amount to  9408 by the end of 2 years (i.e 8400 compounded at 12% for 1 year)

25088-9408-9680 = 6000 

This pdf of simple and compound interest formulae for CAT can be of help to you.