A bag contains Rs 216 in the form of 1 Re, 50 paise and 25 paise coins in the ratio of 2:3:4. The number of 50 paise coins is

Options

A. 140
B. 175
C. 184
D. 144

Answer

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

### Step 1: Understand the Ratios
The coins are in the ratio of 1 Rupee : 50 Paise : 25 Paise = 2 : 3 : 4.
Let's denote the number of 1 Rupee coins as 2x, the number of 50 Paise coins as 3x, and the number of 25 Paise coins as 4x.

### Step 2: Calculate the Total Value of Each Coin Type
- The value of 1 Rupee coins (2x coins) = 2x * 1 = 2x Rupees
- The value of 50 Paise coins (3x coins) = 3x * 0.50 = 1.5x Rupees
- The value of 25 Paise coins (4x coins) = 4x * 0.25 = 1x Rupees

### Step 3: Write the Total Value Equation
The total value of all coins is given as Rs 216. Therefore, we can write the equation:
\[ 2x + 1.5x + 1x = 216 \]

### Step 4: Combine Like Terms
Combine the terms on the left side:
\[ (2x + 1.5x + 1x) = 4.5x \]
So the equation becomes:
\[ 4.5x = 216 \]

### Step 5: Solve for x
To find the value of x, divide both sides by 4.5:
\[ x = \frac{216}{4.5} = 48 \]

### Step 6: Find the Number of 50 Paise Coins
The number of 50 Paise coins is represented by 3x. Therefore:
\[ \text{Number of 50 Paise coins} = 3x = 3 \times 48 = 144 \]

### Conclusion
The number of 50 Paise coins is **144**.