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 310. Then the number of one rupee coins is

Options

A. 150
B. 105
C. 145
D. 155

Answer

To solve the problem, we need to find the number of one rupee coins given the ratio of different types of coins and the total amount of money. Here’s a step-by-step solution:

### Step 1: Define the variables based on the given ratio
Let the number of one rupee coins be \(2.5x\), the number of fifty paise coins be \(3x\), and the number of twenty-five paise coins be \(4x\).

### Step 2: Convert the values 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 = \(4x \times 0.25 = x\) rupees

### Step 3: Set up the equation for the total amount
According to the problem, the total amount is Rs 310. Therefore, we can write the equation:
\[ 2.5x + 1.5x + x = 310 \]

### Step 4: Combine like terms
Combine the terms on the left side:
\[ (2.5x + 1.5x + x) = 5x \]
So, we have:
\[ 5x = 310 \]

### Step 5: Solve for \(x\)
To find \(x\), divide both sides of the equation by 5:
\[ x = \frac{310}{5} = 62 \]

### Step 6: Find the number of one rupee coins
Now, substitute \(x\) back into the expression for the number of one rupee coins:
\[ \text{Number of one rupee coins} = 2.5x = 2.5 \times 62 \]
Calculating this gives:
\[ 2.5 \times 62 = 155 \]

### Conclusion
The number of one rupee coins is **155**.

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