In a bag, the number 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

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the ratio of coins
The number of Re. 1 coins, 50 paise coins, and 25 paise coins are in the ratio 3:2:4. We can represent the number of these coins as:
- Re. 1 coins = 3k
- 50 paise coins = 2k
- 25 paise coins = 4k

### Step 2: Calculate the total value of the coins
Next, we need to calculate the total value of these coins. We know:
- The value of Re. 1 coins = 3k * 1 = 3k rupees
- The value of 50 paise coins = 2k * 0.5 = k rupees (since 50 paise = 0.5 rupees)
- The value of 25 paise coins = 4k * 0.25 = k rupees (since 25 paise = 0.25 rupees)

### Step 3: Set up the equation for total value
According to the problem, the total value of all the coins is Rs. 50. Therefore, we can set up the equation:
\[ 3k + k + k = 50 \]
This simplifies to:
\[ 5k = 50 \]

### Step 4: Solve for k
Now, we can solve for k:
\[ k = \frac{50}{5} = 10 \]

### Step 5: Find the number of 50 paise coins
Now that we have the value of k, we can find the number of 50 paise coins:
- Number of 50 paise coins = 2k = 2 * 10 = 20

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

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