A bag contains 5, 10, and 20 notes in the ratio 4:7:5. If there are 80 notes in all, find the amount of money in the bag.

Answer

To solve the problem step by step, we will follow the instructions provided in the video transcript.

### Step 1: Understand the Ratio
The notes are in the ratio of 4:7:5. This means:
- For every 4 notes of ₹5, there are 7 notes of ₹10 and 5 notes of ₹20.

### Step 2: Define Variables
Let:
- The number of ₹5 notes be \(4x\)
- The number of ₹10 notes be \(7x\)
- The number of ₹20 notes be \(5x\)

### Step 3: Set Up the Equation
According to the problem, the total number of notes is 80. Therefore, we can set up the equation:
\[ 4x + 7x + 5x = 80 \]

### Step 4: Combine Like Terms
Combine the terms on the left side:
\[ 16x = 80 \]

### Step 5: Solve for \(x\)
To find \(x\), divide both sides by 16:
\[ x = \frac{80}{16} = 5 \]

### Step 6: Calculate the Number of Each Type of Note
Now that we have \(x\), we can find the number of each type of note:
- Number of ₹5 notes: \(4x = 4 \times 5 = 20\)
- Number of ₹10 notes: \(7x = 7 \times 5 = 35\)
- Number of ₹20 notes: \(5x = 5 \times 5 = 25\)

### Step 7: Calculate the Total Amount of Money
Now we will calculate the total amount of money for each type of note:
1. Total money from ₹5 notes:
\[ 20 \text{ notes} \times ₹5 = ₹100 \]
2. Total money from ₹10 notes:
\[ 35 \text{ notes} \times ₹10 = ₹350 \]
3. Total money from ₹20 notes:
\[ 25 \text{ notes} \times ₹20 = ₹500 \]

### Step 8: Sum Up All the Amounts
Finally, add all the amounts together to find the total amount of money in the bag:
\[ ₹100 + ₹350 + ₹500 = ₹950 \]

### Final Answer
The total amount of money in the bag is ₹950.

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