A boy has a few coins of denominations 50 paise, 25 paise and 10 paise in the ratio `1 : 2 : 3`. If the total amount of the coins is Rs 6.50, the number of 10 paise coins is

Options

A. 5
B. 10
C. 15
D. 20

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 boy has coins of three denominations: 50 paise, 25 paise, and 10 paise. The ratio of the number of these coins is given as:
- 50 paise coins = 1 part
- 25 paise coins = 2 parts
- 10 paise coins = 3 parts

Let the number of 50 paise coins be \( K \), then:
- Number of 50 paise coins = \( K \)
- Number of 25 paise coins = \( 2K \)
- Number of 10 paise coins = \( 3K \)

### Step 2: Convert Denominations to Rupees
Next, we convert the denominations from paise to rupees:
- 50 paise = \( 0.50 \) rupees
- 25 paise = \( 0.25 \) rupees
- 10 paise = \( 0.10 \) rupees

### Step 3: Calculate Total Value of Coins
Now, we can express the total value of the coins in rupees:
- Total value from 50 paise coins = \( 0.50 \times K \)
- Total value from 25 paise coins = \( 0.25 \times 2K = 0.50K \)
- Total value from 10 paise coins = \( 0.10 \times 3K = 0.30K \)

### Step 4: Set Up the Equation
The total value of all the coins is given as Rs 6.50. Therefore, we can set up the equation:
\[ 0.50K + 0.50K + 0.30K = 6.50 \]

### Step 5: Simplify the Equation
Combining the terms on the left side:
\[ (0.50 + 0.50 + 0.30)K = 6.50 \]
\[ 1.30K = 6.50 \]

### Step 6: Solve for \( K \)
Now, we can solve for \( K \):
\[ K = \frac{6.50}{1.30} = 5 \]

### Step 7: Find the Number of 10 Paise Coins
The number of 10 paise coins is given by \( 3K \):
\[ \text{Number of 10 paise coins} = 3K = 3 \times 5 = 15 \]

### Final Answer
Thus, the number of 10 paise coins is **15**.

---