A purse contains रु1 and 2 coins in the ratio 7:4. If there are 242 coins in the purse, find the total amount of money in the purse.

Answer

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

### Step 1: Understand the Ratio
We are given that the ratio of ₹1 coins to ₹2 coins is 7:4. This means for every 7 ₹1 coins, there are 4 ₹2 coins.

### Step 2: Set Up Variables
Let:
- \( X \) = number of ₹1 coins
- \( Y \) = number of ₹2 coins

According to the ratio, we can write:
\[ \frac{X}{Y} = \frac{7}{4} \]

### Step 3: Express Y in Terms of X
From the ratio, we can express \( Y \) in terms of \( X \):
\[ Y = \frac{4}{7}X \]

### Step 4: Total Number of Coins
We know that the total number of coins is 242. Therefore, we can write:
\[ X + Y = 242 \]

### Step 5: Substitute Y in the Total Equation
Now, substitute \( Y \) from Step 3 into the total equation:
\[ X + \frac{4}{7}X = 242 \]

### Step 6: Combine Like Terms
To combine the terms, convert \( X \) into a fraction:
\[ \frac{7}{7}X + \frac{4}{7}X = 242 \]
This simplifies to:
\[ \frac{11}{7}X = 242 \]

### Step 7: Solve for X
To isolate \( X \), multiply both sides by \( \frac{7}{11} \):
\[ X = 242 \times \frac{7}{11} \]

Calculating \( 242 \div 11 \):
\[ 242 \div 11 = 22 \]
Now, multiply by 7:
\[ X = 22 \times 7 = 154 \]

### Step 8: Find Y
Now that we have \( X \), we can find \( Y \):
\[ Y = 242 - X = 242 - 154 = 88 \]

### Step 9: Calculate Total Amount of Money
Now we can calculate the total amount of money in the purse:
\[ \text{Total Amount} = (X \times 1) + (Y \times 2) \]
Substituting the values of \( X \) and \( Y \):
\[ \text{Total Amount} = (154 \times 1) + (88 \times 2) = 154 + 176 = 330 \]

### Final Answer
The total amount of money in the purse is **₹330**.

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