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 ₹ 210. The number of one rupee coin is

Options

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

Answer

To solve the problem, we need to find the number of one rupee coins given the ratios of the coins and the total amount. Here's a step-by-step solution:

### Step 1: Understand the Ratios
The number of coins is given in the ratio of 2.5:3:4. Let's denote:
- The number of one rupee coins as \(2.5x\)
- The number of fifty paise coins as \(3x\)
- The number of twenty-five paise coins as \(4x\)

### Step 2: Convert the Coin Values to Rupees
Next, we convert the values of the coins into rupees:
- The value of one rupee coins: \(2.5x \times 1 = 2.5x\) rupees
- The value of fifty paise coins: \(3x \times 0.5 = 1.5x\) rupees
- The value of twenty-five paise coins: \(4x \times 0.25 = 1x\) rupees

### Step 3: Set Up the Total Amount Equation
Now, we can write the equation for the total amount:
\[ 2.5x + 1.5x + 1x = 210 \]

### Step 4: Combine Like Terms
Combine the terms on the left side:
\[ 5x = 210 \]

### Step 5: Solve for \(x\)
Now, divide both sides by 5 to find \(x\):
\[ x = \frac{210}{5} = 42 \]

### Step 6: Find the Number of One Rupee Coins
Now that we have \(x\), we can find the number of one rupee coins:
\[ \text{Number of one rupee coins} = 2.5x = 2.5 \times 42 = 105 \]

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

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