A bag contains Rs 90 In coins of denominations of 50 paise, 25 palse and 10 palse. If coins of 50 palse, 25 palse and 10 palse are In the ratio `2:3:5`, then the number of 25 paise coins in the bag is

Options

A. 80
B. 120
C. 100
D. 135

Answer

To solve the problem, we need to find the number of 25 paise coins in a bag that contains Rs. 90 in coins of denominations of 50 paise, 25 paise, and 10 paise, which are in the ratio of 2:3:5.

### Step-by-Step Solution:

1. **Understand the Ratio**:
The ratio of the number of coins of 50 paise, 25 paise, and 10 paise is given as 2:3:5. Let the number of 50 paise coins be \(2x\), the number of 25 paise coins be \(3x\), and the number of 10 paise coins be \(5x\).

2. **Convert the Denominations to Rupees**:
- The value of 50 paise coins:
\[ \text{Value} = 2x \times 0.50 = x \text{ Rupees} \]
- The value of 25 paise coins:
\[ \text{Value} = 3x \times 0.25 = 0.75x \text{ Rupees} \]
- The value of 10 paise coins:
\[ \text{Value} = 5x \times 0.10 = 0.50x \text{ Rupees} \]

3. **Calculate the Total Value**:
Now, we can sum the values of all coins:
\[ \text{Total Value} = x + 0.75x + 0.50x = 2.25x \text{ Rupees} \]

4. **Set Up the Equation**:
We know the total value of the coins is Rs. 90. Therefore, we can set up the equation:
\[ 2.25x = 90 \]

5. **Solve for \(x\)**:
To find \(x\), divide both sides of the equation by 2.25:
\[ x = \frac{90}{2.25} = 40 \]

6. **Find the Number of 25 Paise Coins**:
Now that we have \(x\), we can find the number of 25 paise coins:
\[ \text{Number of 25 paise coins} = 3x = 3 \times 40 = 120 \]

### Final Answer:
The number of 25 paise coins in the bag is **120**.