In a cricket match, Team A scored 232 runs without losing a wicket. The score consisted to byes, wides and runs scored by two opening batsmen : Ram and Shyam. The runs scored by the two batsman are 26 times wides. There are 8 more byes than wides. If the ratio of the runs scored by Ram and Shyam is `6:7`, then the runs scored by Ram is

Options

A. 88
B. 96
C. 102
D. 112

Answer

To solve the problem step by step, we need to set up equations based on the information provided.

### Step-by-Step Solution:

1. **Define Variables:**
Let the number of runs scored by wides be \( x \).

2. **Calculate Runs Scored by Batsmen:**
According to the problem, the runs scored by the two batsmen (Ram and Shyam) is 26 times the runs scored by wides. Therefore, the runs scored by Ram and Shyam together can be expressed as:
\[ \text{Runs by Ram and Shyam} = 26x \]

3. **Calculate Runs Scored by Byes:**
The problem states that there are 8 more byes than wides. Thus, the runs scored by byes can be expressed as:
\[ \text{Runs by Byes} = x + 8 \]

4. **Set Up the Total Runs Equation:**
The total runs scored by Team A is 232. Therefore, we can set up the following equation:
\[ x + 26x + (x + 8) = 232 \]
Simplifying this gives:
\[ 28x + 8 = 232 \]

5. **Solve for \( x \):**
Subtract 8 from both sides:
\[ 28x = 224 \]
Now, divide both sides by 28:
\[ x = 8 \]

6. **Calculate Runs Scored by Batsmen:**
Now that we have \( x \), we can find the runs scored by Ram and Shyam:
\[ \text{Runs by Ram and Shyam} = 26x = 26 \times 8 = 208 \]

7. **Determine the Ratio of Runs Scored:**
The ratio of runs scored by Ram and Shyam is given as \( 6:7 \). The total parts in the ratio is:
\[ 6 + 7 = 13 \]

8. **Calculate Runs Scored by Ram:**
To find the runs scored by Ram, we use the ratio:
\[ \text{Runs by Ram} = \frac{6}{13} \times 208 \]
Calculating this gives:
\[ \text{Runs by Ram} = \frac{6 \times 208}{13} = \frac{1248}{13} = 96 \]

### Final Answer:
The runs scored by Ram is \( 96 \).