The traffic police recorded the speed (in km/hr) of 10 motorcyclists as 32, 45, 46, 55, 65 , 38, 45, 41 , 39 and 62. Later on, an error in recording instrument was found. Find the correct average speed of the motorcyclists, if the instrument recorded 3 km/hr less in each case.

Options

A. 49.9 km/hr
B. 48.5 km/hr
C. 43.8 km/hr
D. 49.8 km/hr

Answer

To find the correct average speed of the motorcyclists after correcting the error in the speed recording, we can follow these steps:

### Step 1: List the recorded speeds
The recorded speeds of the 10 motorcyclists are:
- 32, 45, 46, 55, 65, 38, 45, 41, 39, 62

### Step 2: Correct the recorded speeds
Since the instrument recorded 3 km/hr less in each case, we need to add 3 km/hr to each recorded speed to find the actual speeds.

The corrected speeds will be:
- 32 + 3 = 35
- 45 + 3 = 48
- 46 + 3 = 49
- 55 + 3 = 58
- 65 + 3 = 68
- 38 + 3 = 41
- 45 + 3 = 48
- 41 + 3 = 44
- 39 + 3 = 42
- 62 + 3 = 65

So, the corrected speeds are:
- 35, 48, 49, 58, 68, 41, 48, 44, 42, 65

### Step 3: Calculate the sum of the corrected speeds
Now, we will sum up the corrected speeds:
- Sum = 35 + 48 + 49 + 58 + 68 + 41 + 48 + 44 + 42 + 65

Calculating the sum:
- Sum = 35 + 48 = 83
- Sum = 83 + 49 = 132
- Sum = 132 + 58 = 190
- Sum = 190 + 68 = 258
- Sum = 258 + 41 = 299
- Sum = 299 + 48 = 347
- Sum = 347 + 44 = 391
- Sum = 391 + 42 = 433
- Sum = 433 + 65 = 498

So, the total sum of the corrected speeds is 498 km/hr.

### Step 4: Calculate the average speed
To find the average speed, we divide the total sum of the corrected speeds by the number of motorcyclists (which is 10):
- Average speed = Total sum of corrected speeds / Number of motorcyclists
- Average speed = 498 / 10 = 49.8 km/hr

### Final Answer
The correct average speed of the motorcyclists is **49.8 km/hr**.

---