A man has Rs.640 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. 100
B. 120
C. 40
D. 80

Answer

To solve the problem, we will follow these steps:

1. **Define Variables**: Let the number of one-rupee notes, five-rupee notes, and ten-rupee notes each be represented by \( x \). Since the number of notes of each denomination is equal, we have:
- Number of one-rupee notes = \( x \)
- Number of five-rupee notes = \( x \)
- Number of ten-rupee notes = \( x \)

2. **Calculate Total Value**: The total value contributed by each denomination 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 = \( 10 \times x = 10x \)

3. **Set Up the Equation**: The total value of all the notes is given as Rs. 640. Therefore, we can set up the equation:
\[ x + 5x + 10x = 640 \]

4. **Combine Like Terms**: Combine the terms on the left side of the equation:
\[ 16x = 640 \]

5. **Solve for \( x \)**: To find the value of \( x \), divide both sides by 16:
\[ x = \frac{640}{16} = 40 \]

6. **Calculate Total Number of Notes**: Since \( x \) represents the number of notes of each denomination, the total number of notes is:
\[ \text{Total number of notes} = x + x + x = 3x = 3 \times 40 = 120 \]

Thus, the total number of notes that the man has is **120**.