A hostel charges a fixed amount for the month plus a fixed amount for every day a student takes meals. Vikram took meals for 25 days and paid Rs 4500 in all, while Salman took meals for 30 days and paid Rs 5000. Find the fixed monthly charge (in Rs).

Let the fixed charge be Rs $x$ and the daily meal charge Rs $y.x+25y=4500$ and $x+30y=5000$. Subtracting: $5y=500$, so $y=100$ and $x=4500-2500=2000$. Check: $2000+30\times 100=5000$. 100 is the daily meal charge, the other unknown; 180 comes from dividing Vikram's whole bill by his 25 days, which wrongly treats the fixed charge as part of the daily rate; 2500 is only the meal part of Vikram's bill.