A passenger is charged Rs. 2250 for a cab. The cab owner charge Rs. 500 /- for the 1st hour. For every other hour he charges Rs. 50 less than the previous hour. Find the number of hours for which the passenger rides the cab.

Answer

To solve the problem step by step, we need to calculate the total fare charged for each hour the passenger rides the cab, and then find out how many hours it takes to reach the total fare of Rs. 2250.

### Step 1: Understand the fare structure
- The fare for the first hour is Rs. 500.
- For each subsequent hour, the fare decreases by Rs. 50.

### Step 2: Write down the fare for each hour
- 1st hour: Rs. 500
- 2nd hour: Rs. 500 - Rs. 50 = Rs. 450
- 3rd hour: Rs. 450 - Rs. 50 = Rs. 400
- 4th hour: Rs. 400 - Rs. 50 = Rs. 350
- 5th hour: Rs. 350 - Rs. 50 = Rs. 300
- 6th hour: Rs. 300 - Rs. 50 = Rs. 250

### Step 3: Calculate the total fare for each hour cumulatively
- After 1 hour: Rs. 500
- After 2 hours: Rs. 500 + Rs. 450 = Rs. 950
- After 3 hours: Rs. 950 + Rs. 400 = Rs. 1350
- After 4 hours: Rs. 1350 + Rs. 350 = Rs. 1700
- After 5 hours: Rs. 1700 + Rs. 300 = Rs. 2000
- After 6 hours: Rs. 2000 + Rs. 250 = Rs. 2250

### Step 4: Conclusion
The total fare after 6 hours is Rs. 2250, which matches the amount charged to the passenger.

Thus, the passenger rode the cab for **6 hours**.