A bag contains 25 paise 10 paise and 5 paise coins in the ratio 1:2:3 if their total value is Rs.30 the number of 5 paise coins is

Options

A. 50
B. 100
C. 150
D. 200

Answer

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

### Step 1: Understand the Ratios
We are given that the number of 25 paise, 10 paise, and 5 paise coins are in the ratio of 1:2:3. Let's denote the number of 25 paise coins as \( x \), the number of 10 paise coins as \( 2x \), and the number of 5 paise coins as \( 3x \).

### Step 2: Calculate the Total Value in Paise
The total value of the coins is given as Rs. 30. To work with the values easily, we convert Rs. 30 into paise:
\[ 30 \text{ Rs} = 30 \times 100 = 3000 \text{ paise} \]

### Step 3: Calculate the Value of Each Type of Coin
Now, we can calculate the total value contributed by each type of coin:
- The value from 25 paise coins: \( 25 \times x \)
- The value from 10 paise coins: \( 10 \times 2x = 20x \)
- The value from 5 paise coins: \( 5 \times 3x = 15x \)

### Step 4: Set Up the Equation
Now, we can set up the equation based on the total value:
\[ 25x + 20x + 15x = 3000 \]
Combine the terms:
\[ 60x = 3000 \]

### Step 5: Solve for \( x \)
Now, we can solve for \( x \):
\[ x = \frac{3000}{60} = 50 \]

### Step 6: Find the Number of 5 Paise Coins
Since the number of 5 paise coins is \( 3x \):
\[ 3x = 3 \times 50 = 150 \]

Thus, the number of 5 paise coins is **150**.

### Final Answer
The number of 5 paise coins is **150**.

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