A man has Rs.312 in the denominations of one-rupee notes, five-rupee notes and twenty-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has?

Options

A. 36
B. 24
C. 28
D. 32

Answer

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

### Step 1: Define the Variables
Let the number of notes of each denomination (one-rupee, five-rupee, and twenty-rupee) be represented by \( x \).

### Step 2: Calculate the Total Value of the Notes
The total value contributed by each denomination can be expressed as:
- Value from one-rupee notes: \( 1 \times x = x \)
- Value from five-rupee notes: \( 5 \times x = 5x \)
- Value from twenty-rupee notes: \( 20 \times x = 20x \)

### Step 3: Set Up the Equation
The total amount of money he has is Rs. 312. Therefore, we can set up the equation:
\[ x + 5x + 20x = 312 \]

### Step 4: Simplify the Equation
Combine like terms:
\[ 26x = 312 \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides of the equation by 26:
\[ x = \frac{312}{26} \]
Calculating this gives:
\[ x = 12 \]

### Step 6: Calculate the Total Number of Notes
Since \( x \) represents the number of notes for each denomination, the total number of notes is:
\[ \text{Total notes} = 3x = 3 \times 12 = 36 \]

### Final Answer
The total number of notes that he has is **36**.

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