In a bag, the numbers of Re 1 coins, 50 paise coins and 25 paise coins are in the ratio 3:2:4. the total value of the coins in it is Rs 50. Find the number of 50 paise coins in it.

Options

A. 10
B. 20
C. 30
D. 40

Explanation

To solve the problem, we will follow these steps:

### Step 1: Define the Variables
Let the number of Re 1 coins be \(3x\), the number of 50 paise coins be \(2x\), and the number of 25 paise coins be \(4x\). Here, \(x\) is a common multiplier.

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

### Step 3: Set Up the Equation for Total Value
The total value of all the coins is given as Rs 50. Therefore, we can write the equation:
\[ 3x + x + x = 50 \]

### Step 4: Simplify the Equation
Combining like terms:
\[ 5x = 50 \]

### Step 5: Solve for \(x\)
To find \(x\), divide both sides by 5:
\[ x = \frac{50}{5} = 10 \]

### Step 6: Calculate the Number of 50 Paise Coins
Now, substitute \(x\) back to find the number of 50 paise coins:
\[ \text{Number of 50 paise coins} = 2x = 2 \times 10 = 20 \]

### Final Answer
The number of 50 paise coins in the bag is **20**.

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