A bag contains 1 , 50 paise and 25 paise coins in the ratio of 8:9:11. If the total money in the bag is X 366, then find the number of 25 paise coins.

Options

A. 264
B. 364
C. 241
D. 254

Answer

To solve the problem step by step, we will follow the given information about the coins and their ratios.

### Step 1: Understand the Ratios
The coins in the bag are in the ratio of 1 rupee coins to 50 paise coins to 25 paise coins as 8:9:11.

### Step 2: Define Variables
Let the number of 1 rupee coins be \(8k\), the number of 50 paise coins be \(9k\), and the number of 25 paise coins be \(11k\), where \(k\) is a common multiplier.

### Step 3: Calculate the Total Value of Each Type of Coin
- The value of 1 rupee coins:
\[ \text{Value} = 8k \times 1 = 8k \text{ rupees} \]
- The value of 50 paise coins:
\[ \text{Value} = 9k \times 0.50 = 9k \times \frac{1}{2} = \frac{9k}{2} \text{ rupees} \]
- The value of 25 paise coins:
\[ \text{Value} = 11k \times 0.25 = 11k \times \frac{1}{4} = \frac{11k}{4} \text{ rupees} \]

### Step 4: Write the Total Value Equation
The total value of all coins is given as 366 rupees. Therefore, we can write:
\[ 8k + \frac{9k}{2} + \frac{11k}{4} = 366 \]

### Step 5: Find a Common Denominator
The least common multiple of the denominators (1, 2, and 4) is 4. We can multiply the entire equation by 4 to eliminate the fractions:
\[ 4 \times 8k + 4 \times \frac{9k}{2} + 4 \times \frac{11k}{4} = 4 \times 366 \]
This simplifies to:
\[ 32k + 18k + 11k = 1464 \]

### Step 6: Combine Like Terms
Now, combine the terms on the left side:
\[ (32k + 18k + 11k) = 61k \]
So we have:
\[ 61k = 1464 \]

### Step 7: Solve for \(k\)
Now, divide both sides by 61 to find \(k\):
\[ k = \frac{1464}{61} = 24 \]

### Step 8: Find the Number of 25 Paise Coins
Now that we have \(k\), we can find the number of 25 paise coins:
\[ \text{Number of 25 paise coins} = 11k = 11 \times 24 = 264 \]

### Final Answer
The number of 25 paise coins in the bag is **264**.

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