A batsman scored 110 runs which included 3 boundaries and 8 sixes. What per cent of his total score, did he make by running between the wickets?

Options

A. 45%
B. `45(5)/(11)`
C. `54 (6)/(11)%`
D. 55%

Answer

To solve the problem step by step, we will calculate the runs scored by the batsman through boundaries and sixes, then determine the runs made by running between the wickets, and finally calculate the percentage of those runs relative to the total score.

### Step-by-Step Solution:

1. **Identify the total runs scored by the batsman**:
The batsman scored a total of 110 runs.

2. **Calculate the runs scored from boundaries**:
A boundary is worth 4 runs. The batsman hit 3 boundaries.
\[ \text{Runs from boundaries} = 3 \text{ boundaries} \times 4 \text{ runs/boundary} = 12 \text{ runs} \]

3. **Calculate the runs scored from sixes**:
A six is worth 6 runs. The batsman hit 8 sixes.
\[ \text{Runs from sixes} = 8 \text{ sixes} \times 6 \text{ runs/six} = 48 \text{ runs} \]

4. **Calculate the total runs scored from boundaries and sixes**:
\[ \text{Total runs from boundaries and sixes} = 12 \text{ runs} + 48 \text{ runs} = 60 \text{ runs} \]

5. **Calculate the runs made by running between the wickets**:
To find the runs made by running, we subtract the runs from boundaries and sixes from the total runs.
\[ \text{Runs by running} = \text{Total runs} - \text{Total runs from boundaries and sixes} \]
\[ \text{Runs by running} = 110 \text{ runs} - 60 \text{ runs} = 50 \text{ runs} \]

6. **Calculate the percentage of runs made by running between the wickets**:
The percentage is calculated using the formula:
\[ \text{Percentage} = \left( \frac{\text{Runs by running}}{\text{Total runs}} \right) \times 100 \]
\[ \text{Percentage} = \left( \frac{50}{110} \right) \times 100 \]
Simplifying this:
\[ \text{Percentage} = \frac{5000}{110} \approx 45.45\% \]

### Final Answer:
The percentage of his total score that he made by running between the wickets is approximately **45.45%**.