A man has 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?

Options

A. 45
B. 60
C. 75
D. 90

Answer

To solve the problem step by step, we will follow these instructions:

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

### Step 2: Express the total value of the notes
The total value of the notes can be expressed as follows:
- Value from one-rupee notes = \( 1 \times x = x \)
- Value from five-rupee notes = \( 5 \times x = 5x \)
- Value from ten-rupee notes = \( 10 \times x = 10x \)

### Step 3: Set up the equation
The total value of all the notes is given as 480. Therefore, we can write the equation:
\[ x + 5x + 10x = 480 \]

### Step 4: Combine like terms
Combine the terms on the left side of the equation:
\[ 16x = 480 \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides of the equation by 16:
\[ x = \frac{480}{16} = 30 \]

### Step 6: Calculate the total number of notes
Since there are three denominations of notes and each denomination has \( x \) notes, the total number of notes is:
\[ \text{Total notes} = 3x = 3 \times 30 = 90 \]

### Final Answer
The total number of notes that the man has is **90**.

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