A bag contains 50 paise , 1 rupee and 2 rupee coins in the ratio 2 : 3: 4 . If the total amount is rupes 240 what is the total number of coins?

Answer

To solve the problem step by step, we will follow the given information about the coins and their ratios.

### Step-by-Step Solution:

1. **Understand the Ratios**:
The coins are in the ratio of 50 paise : 1 rupee : 2 rupees = 2 : 3 : 4.

2. **Assign Variables**:
Let the number of 50 paise coins be \(2x\), the number of 1 rupee coins be \(3x\), and the number of 2 rupee coins be \(4x\).

3. **Convert Coin Values to Rupees**:
- The value of 50 paise coins = \(0.5 \times 2x = x\) rupees.
- The value of 1 rupee coins = \(1 \times 3x = 3x\) rupees.
- The value of 2 rupee coins = \(2 \times 4x = 8x\) rupees.

4. **Set Up the Equation**:
The total amount in the bag is given as 240 rupees. Therefore, we can write the equation:
\[ x + 3x + 8x = 240 \]

5. **Combine Like Terms**:
Combine the terms on the left side of the equation:
\[ 12x = 240 \]

6. **Solve for \(x\)**:
Divide both sides by 12:
\[ x = \frac{240}{12} = 20 \]

7. **Find the Number of Each Type of Coin**:
- Number of 50 paise coins = \(2x = 2 \times 20 = 40\)
- Number of 1 rupee coins = \(3x = 3 \times 20 = 60\)
- Number of 2 rupee coins = \(4x = 4 \times 20 = 80\)

8. **Calculate the Total Number of Coins**:
The total number of coins is:
\[ 40 + 60 + 80 = 180 \]

### Final Answer:
The total number of coins is **180**.

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