The ratio of number of 10 rupee notes to 20 rupee notes in a purse is 3:4. If there are total 84 notes in the purse, then how much money is there in the purse?

Options

A. Rs 1320
B. Rs 1230
C. Rs 1100
D. Rs 1260

Answer

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

### Step 1: Understand the ratio
The ratio of the number of 10 rupee notes to 20 rupee notes is given as 3:4. This means for every 3 notes of 10 rupees, there are 4 notes of 20 rupees.

### Step 2: Define variables
Let the number of 10 rupee notes be \(3k\) and the number of 20 rupee notes be \(4k\), where \(k\) is a common multiplier.

### Step 3: Set up the equation
According to the problem, the total number of notes is 84. Therefore, we can write the equation:
\[ 3k + 4k = 84 \]

### Step 4: Combine like terms
Combine the terms on the left side:
\[ 7k = 84 \]

### Step 5: Solve for \(k\)
To find \(k\), divide both sides of the equation by 7:
\[ k = \frac{84}{7} = 12 \]

### Step 6: Find the number of notes
Now, substitute \(k\) back to find the number of 10 rupee and 20 rupee notes:
- Number of 10 rupee notes:
\[ 3k = 3 \times 12 = 36 \]
- Number of 20 rupee notes:
\[ 4k = 4 \times 12 = 48 \]

### Step 7: Calculate the total money
Now, we calculate the total amount of money in the purse:
- Total value of 10 rupee notes:
\[ 36 \times 10 = 360 \text{ rupees} \]
- Total value of 20 rupee notes:
\[ 48 \times 20 = 960 \text{ rupees} \]

### Step 8: Add the total values
Finally, add the values of both types of notes to find the total money in the purse:
\[ 360 + 960 = 1320 \text{ rupees} \]

### Final Answer
The total amount of money in the purse is **1320 rupees**.

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