What are the marks obtained by Arnab in History ?
I. The average makes obtained by Arnab in History, Geography and Civics are 65.
II. Marks obtained by Arnab in Geography is 6 more than that obtained in History.
III. Marks obtained in Geography is as much more than that in Civics as teh marks obtained in Civics is more than that in History.

Options

A. I and II
B. II and III
C. I and III
D. None of these

Explanation

To find out the marks obtained by Arnab in History, we will analyze the statements provided step by step.

### Step 1: Analyze Statement I
The first statement tells us that the average marks obtained by Arnab in History, Geography, and Civics is 65.

Using the formula for average:
\[ \text{Average} = \frac{\text{Total Marks}}{\text{Number of Subjects}} \]
We can express this as:
\[ \frac{H + G + C}{3} = 65 \]
Multiplying both sides by 3 gives:
\[ H + G + C = 195 \quad \text{(Equation 1)} \]

### Step 2: Analyze Statement II
The second statement states that the marks obtained by Arnab in Geography is 6 more than that obtained in History.

Let’s denote the marks in History as \( H \). Then, the marks in Geography can be expressed as:
\[ G = H + 6 \quad \text{(Equation 2)} \]

### Step 3: Analyze Statement III
The third statement says that the marks obtained in Geography is as much more than that in Civics as the marks obtained in Civics is more than that in History.

This can be expressed mathematically as:
\[ G - C = C - H \]
Rearranging gives:
\[ G + H = 2C \quad \text{(Equation 3)} \]

### Step 4: Substitute Equations
Now we have three equations:
1. \( H + G + C = 195 \)
2. \( G = H + 6 \)
3. \( G + H = 2C \)

Substituting Equation 2 into Equation 1:
\[ H + (H + 6) + C = 195 \]
This simplifies to:
\[ 2H + C + 6 = 195 \]
Subtracting 6 from both sides:
\[ 2H + C = 189 \quad \text{(Equation 4)} \]

Next, substitute Equation 2 into Equation 3:
\[ (H + 6) + H = 2C \]
This simplifies to:
\[ 2H + 6 = 2C \]
Dividing everything by 2 gives:
\[ H + 3 = C \quad \text{(Equation 5)} \]

### Step 5: Substitute C in Equation 4
Now we can substitute Equation 5 into Equation 4:
\[ 2H + (H + 3) = 189 \]
This simplifies to:
\[ 3H + 3 = 189 \]
Subtracting 3 from both sides:
\[ 3H = 186 \]
Dividing by 3 gives:
\[ H = 62 \]

### Conclusion
The marks obtained by Arnab in History is **62**.