465 coins consists of 1 rupee, 50 paise and 25 paise coins. Their values are in the ratio 5:3:1. The number of each type of coins respectively is,

Options

A. `155,186,124`
B. `154,187,124`
C. `154, 185,126`
D. `150,140,175`

Answer

To solve the problem, we need to determine the number of each type of coin (1 rupee, 50 paise, and 25 paise) given that their values are in the ratio of 5:3:1 and the total number of coins is 465.

### Step-by-Step Solution:

1. **Define Variables Based on Ratios**:
Let the number of 1 rupee coins be \(5x\), the number of 50 paise coins be \(3x\), and the number of 25 paise coins be \(x\). This is based on the given ratio of their values (5:3:1).

2. **Set Up the Equation**:
Since the total number of coins is 465, we can set up the following equation:
\[ 5x + 3x + x = 465 \]

3. **Combine Like Terms**:
Combine the terms on the left side of the equation:
\[ 9x = 465 \]

4. **Solve for \(x\)**:
To find \(x\), divide both sides of the equation by 9:
\[ x = \frac{465}{9} = 51.67 \]
However, since we are dealing with whole coins, we should check our calculations. Let's recalculate:
\[ 9x = 465 \implies x = \frac{465}{9} = 51.67 \text{ (which is incorrect)} \]
Let's correct this:
\[ 9x = 465 \implies x = 51 \]

5. **Calculate the Number of Each Type of Coin**:
Now, we can find the number of each type of coin:
- Number of 1 rupee coins: \(5x = 5 \times 31 = 155\)
- Number of 50 paise coins: \(3x = 3 \times 31 = 93\)
- Number of 25 paise coins: \(x = 31\)

6. **Final Answer**:
Therefore, the number of each type of coin is:
- 1 rupee coins: 155
- 50 paise coins: 93
- 25 paise coins: 31