Joseph scored 8 marks fewer than Amit in an examination. Kumar scored 12 marks more than Amit. In total, they scored 205 marks. What was the score of Joseph?

Options

A. 67
B. 79
C. 59
D. 75

Answer

To solve the problem step by step, we will define the variables and set up equations based on the information given.

### Step 1: Define Variables
Let \( x \) be the score of Amit.

### Step 2: Express Joseph's Score
Joseph scored 8 marks fewer than Amit. Therefore, Joseph's score can be expressed as:
\[ \text{Joseph's score} = x - 8 \]

### Step 3: Express Kumar's Score
Kumar scored 12 marks more than Amit. Therefore, Kumar's score can be expressed as:
\[ \text{Kumar's score} = x + 12 \]

### Step 4: Set Up the Total Score Equation
According to the problem, the total score of Joseph, Amit, and Kumar is 205 marks. We can write the equation as:
\[ \text{Amit's score} + \text{Joseph's score} + \text{Kumar's score} = 205 \]
Substituting the expressions we have:
\[ x + (x - 8) + (x + 12) = 205 \]

### Step 5: Simplify the Equation
Now, combine like terms:
\[ x + x - 8 + x + 12 = 205 \]
This simplifies to:
\[ 3x + 4 = 205 \]

### Step 6: Solve for \( x \)
Subtract 4 from both sides:
\[ 3x = 205 - 4 \]
\[ 3x = 201 \]
Now, divide both sides by 3:
\[ x = \frac{201}{3} = 67 \]

### Step 7: Find Joseph's Score
Now that we have Amit's score, we can find Joseph's score:
\[ \text{Joseph's score} = x - 8 = 67 - 8 = 59 \]

### Final Answer
Joseph's score is \( 59 \) marks.

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