A bag contains 1 rupee, 50 paise and 25 paise coins in the ratio `4 : 7 : 5` respectively. If the total amount in the bag is Rs. 280, then find the number of 50 paise coins in the bag.

Options

A. 112
B. 224
C. 160
D. 128

Answer

To solve the problem step by step, we will first define the variables based on the given ratio of coins and then calculate the total amount.

### Step 1: Define the Variables
Let the number of 1 rupee coins be \(4x\), the number of 50 paise coins be \(7x\), and the number of 25 paise coins be \(5x\), where \(x\) is a common multiplier.

### Step 2: Calculate the Total Amount from Each Type of Coin
- The total value of 1 rupee coins:
\[ \text{Value from 1 rupee coins} = 4x \times 1 = 4x \text{ rupees} \]
- The total value of 50 paise coins:
\[ \text{Value from 50 paise coins} = 7x \times 0.50 = 3.5x \text{ rupees} \]
- The total value of 25 paise coins:
\[ \text{Value from 25 paise coins} = 5x \times 0.25 = 1.25x \text{ rupees} \]

### Step 3: Set Up the Equation for Total Amount
According to the problem, the total amount in the bag is Rs. 280. Therefore, we can set up the equation:
\[ 4x + 3.5x + 1.25x = 280 \]

### Step 4: Combine Like Terms
Now, let's combine the terms on the left side:
\[ (4 + 3.5 + 1.25)x = 280 \]
Calculating the sum:
\[ 8.75x = 280 \]

### Step 5: Solve for \(x\)
To find the value of \(x\), divide both sides by 8.75:
\[ x = \frac{280}{8.75} \]
Calculating this gives:
\[ x = 32 \]

### Step 6: Find the Number of 50 Paise Coins
Now that we have \(x\), we can find the number of 50 paise coins:
\[ \text{Number of 50 paise coins} = 7x = 7 \times 32 = 224 \]

### Final Answer
The number of 50 paise coins in the bag is **224**.

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