A bag contains the amount of Rs. 25.8 in the form of 1 rupee, 50 paise and 10 paise coins and are in the ratio of 3:2:3. How many 50 paise coins are there in the bag?

Options

A. `18`
B. `36`
C. `12`
D. `3`

Answer

To solve the problem, we need to find the number of 50 paise coins in a bag that contains a total of Rs. 25.8 in the form of 1 rupee, 50 paise, and 10 paise coins, with the coins in the ratio of 3:2:3.

### Step-by-step Solution:

1. **Define the variables based on the ratio**:
- Let the number of 1 rupee coins be \(3x\).
- Let the number of 50 paise coins be \(2x\).
- Let the number of 10 paise coins be \(3x\).

2. **Calculate the total value contributed by each type of coin**:
- The total value from 1 rupee coins:
\[ \text{Value from 1 rupee coins} = 3x \times 1 = 3x \text{ rupees} \]
- The total value from 50 paise coins:
\[ \text{Value from 50 paise coins} = 2x \times 0.5 = x \text{ rupees} \]
- The total value from 10 paise coins:
\[ \text{Value from 10 paise coins} = 3x \times 0.1 = 0.3x \text{ rupees} \]

3. **Set up the equation for the total value**:
- The total value of all coins is given as Rs. 25.8. Therefore, we can write the equation:
\[ 3x + x + 0.3x = 25.8 \]

4. **Combine like terms**:
- Combine the terms on the left side:
\[ 4.3x = 25.8 \]

5. **Solve for \(x\)**:
- Divide both sides by 4.3:
\[ x = \frac{25.8}{4.3} = 6 \]

6. **Find the number of 50 paise coins**:
- Since the number of 50 paise coins is \(2x\):
\[ \text{Number of 50 paise coins} = 2 \times 6 = 12 \]

### Final Answer:
The number of 50 paise coins in the bag is **12**.