A library charges a flat fee for the first 4 days a book is kept and an extra fine for every day after that. Rahul kept a book for 9 days and paid Rs 40, while Neha kept one for 6 days and paid Rs 28. Find the fine (in Rs) charged for each extra day.

Let the flat fee be Rs $x$ and the fine per extra day Rs $y$. Rahul had 9 - 4 = 5 extra days and Neha 6 - 4 = 2, so $x+5y=40$ and $x+2y=28$. Subtracting: $3y=12$, so $y=4$ and $x=20$. Check: $20+5\times 4=40$ and $20+2\times 4=28$. 20 is the flat fee, the other unknown; 12 is the difference between the two bills before dividing by the 3 extra days; 3 comes from miscounting the extra days as 6 and 2 instead of 5 and 2.