A bag has Rs. 20.1 in the form of 1 rupee, 50-paise and 10 paise coins in the ratio of `5:3:2`. What is the number of 50-paise coins in the bag ?

Options

A. 9
B. 3
C. 2
D. 4

Answer

To solve the problem, we need to find the number of 50-paise coins in a bag that contains Rs. 20.1 in the form of 1 rupee, 50-paise, and 10-paise coins, given in the ratio of 5:3:2.

### Step-by-Step Solution:

1. **Convert the total amount into paise**:
- Rs. 20.1 = 20.1 * 100 paise = 2010 paise.

2. **Set up the ratio of coins**:
- Let the number of 1 rupee coins be \(5x\), the number of 50-paise coins be \(3x\), and the number of 10-paise coins be \(2x\).

3. **Calculate the total value of the coins**:
- Value from 1 rupee coins = \(5x \times 100\) paise = \(500x\) paise.
- Value from 50-paise coins = \(3x \times 50\) paise = \(150x\) paise.
- Value from 10-paise coins = \(2x \times 10\) paise = \(20x\) paise.

4. **Combine the values**:
- Total value in paise = \(500x + 150x + 20x = 670x\) paise.

5. **Set up the equation**:
- We know the total value is 2010 paise, so we can set up the equation:
\[ 670x = 2010 \]

6. **Solve for \(x\)**:
- Divide both sides by 670:
\[ x = \frac{2010}{670} = 3 \]

7. **Find the number of 50-paise coins**:
- The number of 50-paise coins is \(3x = 3 \times 3 = 9\).

### Final Answer:
The number of 50-paise coins in the bag is **9**.

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