In bag there are coins of 25 paisa, 50 paisa and 1 rupee in the ratio of 3 : 4 : 5. If there are in all ₹31, then how many 1 rupee coins are there in the bag?

Options

A. 12
B. 16
C. 24
D. 20

Answer

To solve the problem, we need to find the number of 1 rupee coins in a bag containing coins of 25 paisa, 50 paisa, and 1 rupee in the ratio of 3:4:5. The total value of the coins is ₹31.

### Step-by-step Solution:

1. **Define the Ratio**:
Let the number of 25 paisa coins be \(3x\), the number of 50 paisa coins be \(4x\), and the number of 1 rupee coins be \(5x\).

2. **Convert Coin Values to Rupees**:
- The value of \(3x\) coins of 25 paisa = \(3x \times 0.25\) = \(0.75x\) rupees.
- The value of \(4x\) coins of 50 paisa = \(4x \times 0.50\) = \(2x\) rupees.
- The value of \(5x\) coins of 1 rupee = \(5x \times 1\) = \(5x\) rupees.

3. **Set Up the Equation**:
The total value of all the coins is given as ₹31. Therefore, we can set up the equation:
\[ 0.75x + 2x + 5x = 31 \]

4. **Combine Like Terms**:
Combine the terms on the left side:
\[ (0.75 + 2 + 5)x = 31 \]
\[ 7.75x = 31 \]

5. **Solve for \(x\)**:
To find \(x\), divide both sides by 7.75:
\[ x = \frac{31}{7.75} \]

6. **Calculate \(x\)**:
Simplifying \(x\):
\[ x = \frac{3100}{775} = 4 \]

7. **Find the Number of 1 Rupee Coins**:
The number of 1 rupee coins is given by \(5x\):
\[ 5x = 5 \times 4 = 20 \]

### Final Answer:
The number of 1 rupee coins in the bag is **20**.