I have one rupee coins, fifty paise coins and twenty five paise coins. The number of coins are in the ratio of 2.5 : 3 : 4. If the total amount is Rs.210. The number of one rupee coins is

Options

A. 90
B. 85
C. 100
D. 105

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Ratios
We are given the ratio of the number of coins:
- One rupee coins = 2.5 parts
- Fifty paise coins = 3 parts
- Twenty-five paise coins = 4 parts

### Step 2: Convert the Ratios to a Common Format
To work with these ratios, we can convert them into whole numbers. Since 2.5 is a decimal, we can multiply all parts by 2 to eliminate the decimal:
- One rupee coins = 2.5 × 2 = 5 parts
- Fifty paise coins = 3 × 2 = 6 parts
- Twenty-five paise coins = 4 × 2 = 8 parts

Now the ratio becomes:
- One rupee coins : Fifty paise coins : Twenty-five paise coins = 5 : 6 : 8

### Step 3: Express the Number of Coins
Let the common multiplier be \( x \). Therefore, we can express the number of coins as:
- One rupee coins = \( 5x \)
- Fifty paise coins = \( 6x \)
- Twenty-five paise coins = \( 8x \)

### Step 4: Calculate the Total Value of Coins
Next, we need to calculate the total value of these coins in rupees:
- Value of one rupee coins = \( 5x \times 1 = 5x \) rupees
- Value of fifty paise coins = \( 6x \times 0.5 = 3x \) rupees
- Value of twenty-five paise coins = \( 8x \times 0.25 = 2x \) rupees

Now, we can add these values together:
\[ \text{Total Value} = 5x + 3x + 2x = 10x \text{ rupees} \]

### Step 5: Set Up the Equation
We know from the problem that the total amount is Rs. 210. Therefore, we can set up the equation:
\[ 10x = 210 \]

### Step 6: Solve for \( x \)
Now, we can solve for \( x \):
\[ x = \frac{210}{10} = 21 \]

### Step 7: Find the Number of One Rupee Coins
Now that we have the value of \( x \), we can find the number of one rupee coins:
\[ \text{Number of one rupee coins} = 5x = 5 \times 21 = 105 \]

### Final Answer
The number of one rupee coins is **105**.

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