A man has in all Rs 640 in the denominations of one-rupee, five-rupee and ten-rupee notes. The number of each type of notes are equal. What is the total number of notes he has ?

Options

A. 150
B. 120
C. 100
D. 90

Answer

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

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

### Step 2: Calculate the total value of each type of note
- The total value of one-rupee notes = \( 1 \times x = x \) rupees
- The total value of five-rupee notes = \( 5 \times x = 5x \) rupees
- The total value of ten-rupee notes = \( 10 \times x = 10x \) rupees

### Step 3: Set up the equation for total money
According to the problem, the total amount of money is Rs 640. Therefore, we can write the equation:
\[ x + 5x + 10x = 640 \]

### Step 4: Simplify the equation
Combine like terms:
\[ 16x = 640 \]

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

### Step 6: Calculate the total number of notes
Since there are three types of notes and the number of each type is \( x \), the total number of notes is:
\[ \text{Total number of notes} = x + x + x = 3x = 3 \times 40 = 120 \]

### Final Answer
The total number of notes he has is **120**.

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