Rs 180 contained In a box consists of one rupee, 50 palse and 25 paise coins in the ratio `2:3:4`. What Is the number of 50 paise coins?

Options

A. 60
B. 120
C. 150
D. 180

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the Ratio
The coins are in the ratio of 2:3:4, which corresponds to:
- Rs. 1 coins = 2 parts
- 50 paise coins = 3 parts
- 25 paise coins = 4 parts

### Step 2: Define Variables
Let the common multiple be \( x \). Therefore, we can express the number of coins as:
- Number of Rs. 1 coins = \( 2x \)
- Number of 50 paise coins = \( 3x \)
- Number of 25 paise coins = \( 4x \)

### Step 3: Calculate the Total Value of Each Coin Type
Next, we calculate the total value contributed by each type of coin:
- Value of Rs. 1 coins = \( 2x \times 1 = 2x \) rupees
- Value of 50 paise coins = \( 3x \times 0.5 = 1.5x \) rupees
- Value of 25 paise coins = \( 4x \times 0.25 = x \) rupees

### Step 4: Set Up the Equation
Now, we can set up an equation based on the total value of all coins:
\[ 2x + 1.5x + x = 180 \]

### Step 5: Simplify the Equation
Combine like terms:
\[ (2x + 1.5x + x) = 4.5x \]
So, we have:
\[ 4.5x = 180 \]

### Step 6: Solve for \( x \)
To find \( x \), divide both sides by 4.5:
\[ x = \frac{180}{4.5} = 40 \]

### Step 7: Find the Number of 50 Paise Coins
Now, substitute \( x \) back to find the number of 50 paise coins:
\[ \text{Number of 50 paise coins} = 3x = 3 \times 40 = 120 \]

### Final Answer
The number of 50 paise coins is **120**.

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