Pankaj got 15 marks less than Charu, and Charu got 5 marks more than Kanta. If their total marks are 112, then marks obtained by Kanta is:

Options

A. 29
B. 39
C. 44
D. 45

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Define Variables
Let the marks obtained by Charu be represented by \( X \).

### Step 2: Express Pankaj's Marks
According to the problem, Pankaj got 15 marks less than Charu. Therefore, Pankaj's marks can be expressed as:
\[ P = X - 15 \]

### Step 3: Express Kanta's Marks
The problem states that Charu got 5 marks more than Kanta. Thus, Kanta's marks can be expressed as:
\[ K = X - 5 \]

### Step 4: Set Up the Equation for Total Marks
The total marks obtained by Pankaj, Charu, and Kanta is given as 112. Therefore, we can write the equation:
\[ P + X + K = 112 \]

Substituting the expressions for P and K into the equation, we get:
\[ (X - 15) + X + (X - 5) = 112 \]

### Step 5: Simplify the Equation
Now, simplify the equation:
\[ X - 15 + X + X - 5 = 112 \]
Combine like terms:
\[ 3X - 20 = 112 \]

### Step 6: Solve for X
Add 20 to both sides of the equation:
\[ 3X = 112 + 20 \]
\[ 3X = 132 \]

Now, divide both sides by 3:
\[ X = \frac{132}{3} \]
\[ X = 44 \]

### Step 7: Calculate Kanta's Marks
Now that we have the value of \( X \), we can find Kanta's marks:
\[ K = X - 5 \]
\[ K = 44 - 5 \]
\[ K = 39 \]

### Final Answer
The marks obtained by Kanta is **39**.

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