A typist while typing the numbers from 600 to 799 mistakenly he typed 8 every time in place of 6. So the total number of times he has typed 8 is :

Options

A. A. 300
B. B. 230
C. C. 180
D. D. none of these

Answer

To solve the problem of how many times the typist mistakenly typed the number 8 instead of 6 while typing numbers from 600 to 799, we can break it down step by step.

### Step-by-Step Solution:

1. **Identify the range of numbers**: We need to consider all the numbers from 600 to 799.

2. **Count occurrences of 6 in the hundreds place**:
- The hundreds digit is 6 for all numbers from 600 to 699.
- There are 100 numbers in this range (600 to 699), so the digit 6 appears 100 times in the hundreds place.

3. **Count occurrences of 6 in the tens place**:
- The tens digit can be 6 for the numbers 660 to 669.
- There are 10 numbers in this range (660, 661, 662, ..., 669), so the digit 6 appears 10 times in the tens place.

4. **Count occurrences of 6 in the units place**:
- The units digit can be 6 for the numbers ending in 6, which are: 606, 616, 626, 636, 646, 656, 666, 676, 686, 696.
- There are 10 occurrences of the digit 6 in the units place.

5. **Total occurrences of 6**:
- Now, we add up all the occurrences of 6:
- Hundreds place: 100
- Tens place: 10
- Units place: 10
- Total = 100 + 10 + 10 = 120.

6. **Conclusion**:
- Since the typist typed 8 every time he should have typed 6, the total number of times he typed 8 is 120.

### Final Answer:
The total number of times the typist has typed 8 is **120**.

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