A purse contains Rs. 50, Rs.10 and Rs. 5 notes in the ratio ` 6 : 3 : 7 ` and total amount in the purse is Rs. 730. Find the number of Rs. 5 notes in the purse.

Options

A. 7
B. 14
C. 21
D. 28

Explanation

To solve the problem step by step, we will use the given ratio of the notes and the total amount in the purse.

### Step 1: Understand the Ratio
The ratio of Rs. 50, Rs. 10, and Rs. 5 notes is given as 6:3:7. This means:
- For every 6 Rs. 50 notes, there are 3 Rs. 10 notes and 7 Rs. 5 notes.

### Step 2: Assign Variables
Let the common multiple be \( x \). Therefore, we can express the number of notes as:
- Number of Rs. 50 notes = \( 6x \)
- Number of Rs. 10 notes = \( 3x \)
- Number of Rs. 5 notes = \( 7x \)

### Step 3: Calculate the Total Amount
Next, we calculate the total amount contributed by each type of note:
- Total amount from Rs. 50 notes = \( 50 \times 6x = 300x \)
- Total amount from Rs. 10 notes = \( 10 \times 3x = 30x \)
- Total amount from Rs. 5 notes = \( 5 \times 7x = 35x \)

### Step 4: Set Up the Equation
Now, we can set up the equation based on the total amount in the purse:
\[ 300x + 30x + 35x = 730 \]

### Step 5: Combine Like Terms
Combine the terms on the left side:
\[ 365x = 730 \]

### Step 6: Solve for \( x \)
Now, divide both sides by 365 to find \( x \):
\[ x = \frac{730}{365} = 2 \]

### Step 7: Find the Number of Rs. 5 Notes
Now that we have \( x \), we can find the number of Rs. 5 notes:
\[ \text{Number of Rs. 5 notes} = 7x = 7 \times 2 = 14 \]

### Final Answer
The number of Rs. 5 notes in the purse is **14**.

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