Solvng transistor circuit
19.86=Ib*R2+0.7V. And this gives the value of Ib to be 0.028mA. But my text book has the value of Ib=15.45 microA. 


If only it was a simple potential divider.


  Why am I getting this much difference in the base current?


Because, as you start drawing base current the collector current rises and drags down point A to a lower value. It's not just a simple potential divider in that respect.

You could iteratively solve this by recalculating the collector voltage to use in the "next step" - clearly it would be lower than 19.86 V and this would lead to a lower base current and that in turn would lead to a lower collector current.

Iterate a few cycles and see what you get. I might suggest you use a spreadsheet.