A purse contains one-rupee, 50 paise ad 25 paise coins in the ratio 4:3:6. fi the total amount in the purse is Rs 28, then find the number of 50 paise coins present in the purse.

Answer

To solve the problem, we need to find the number of 50 paise coins in a purse that contains coins in the ratio of 4:3:6 for one-rupee, 50 paise, and 25 paise coins, respectively, with a total amount of Rs 28.

### Step-by-Step Solution:

1. **Define the Variables:**
Let the number of one-rupee coins be \(4k\), the number of 50 paise coins be \(3k\), and the number of 25 paise coins be \(6k\), where \(k\) is a common multiplier.

2. **Calculate the Total Value:**
The total value contributed by each type of coin can be calculated as follows:
- Value from one-rupee coins: \(4k \times 1 = 4k\) rupees
- Value from 50 paise coins: \(3k \times 0.5 = 1.5k\) rupees
- Value from 25 paise coins: \(6k \times 0.25 = 1.5k\) rupees

3. **Set Up the Equation:**
The total amount in the purse is given as Rs 28. Therefore, we can set up the equation:
\[ 4k + 1.5k + 1.5k = 28 \]

4. **Combine Like Terms:**
Combine the terms on the left side of the equation:
\[ 4k + 1.5k + 1.5k = 7k \]
So, the equation becomes:
\[ 7k = 28 \]

5. **Solve for \(k\):**
Divide both sides by 7 to find \(k\):
\[ k = \frac{28}{7} = 4 \]

6. **Find the Number of 50 Paise Coins:**
Now that we have \(k\), we can find the number of 50 paise coins:
\[ \text{Number of 50 paise coins} = 3k = 3 \times 4 = 12 \]

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

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