A batsman scored 150 runs in a one-day cricket match. He hit 20 fours and 5 sixes. Calculate the percentage of runs he scored by running between the wickets.

Options

A. `25%`
B. `73.33%`
C. `20%`
D. `26.67%`

Answer

To solve the problem step by step, we will calculate the percentage of runs scored by the batsman through running between the wickets.

### Step 1: Calculate the total runs scored by boundaries
The batsman hit 20 fours and 5 sixes. We need to calculate how many runs he scored from these boundaries.

- Runs from fours:
\[ 20 \text{ fours} \times 4 \text{ runs per four} = 80 \text{ runs} \]

- Runs from sixes:
\[ 5 \text{ sixes} \times 6 \text{ runs per six} = 30 \text{ runs} \]

### Step 2: Calculate total runs scored by hitting boundaries
Now, we add the runs scored from fours and sixes to find the total runs scored through boundaries.

\[ \text{Total runs from boundaries} = 80 \text{ runs} + 30 \text{ runs} = 110 \text{ runs} \]

### Step 3: Calculate runs scored by running
The batsman scored a total of 150 runs. To find the runs scored by running between the wickets, we subtract the runs scored from boundaries from the total runs.

\[ \text{Runs scored by running} = \text{Total runs} - \text{Total runs from boundaries} \]
\[ \text{Runs scored by running} = 150 \text{ runs} - 110 \text{ runs} = 40 \text{ runs} \]

### Step 4: Calculate the percentage of runs scored by running
To find the percentage of runs scored by running, we use the formula:

\[ \text{Percentage of runs by running} = \left( \frac{\text{Runs scored by running}}{\text{Total runs}} \right) \times 100 \]
\[ \text{Percentage of runs by running} = \left( \frac{40}{150} \right) \times 100 \]

### Step 5: Simplify the fraction and calculate the percentage
Now, we simplify the fraction:

\[ \frac{40}{150} = \frac{4}{15} \]

Calculating \( \frac{4}{15} \times 100 \):

\[ \frac{4 \times 100}{15} = \frac{400}{15} \approx 26.67\% \]

### Final Answer
The percentage of runs scored by the batsman through running between the wickets is approximately **26.67%**.

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