Rs180 contained in a box of one rupee, 50 paise and 25 paise coins in the ratio 2:3:4. What is the number of 50 paise coins?

Options

A. 80
B. 160
C. 120
D. 180

Answer

To solve the problem step by step, we need to find the number of 50 paise coins in a box containing Rs. 180 in the ratio of Rs. 1, Rs. 50, and Rs. 25 coins as 2:3:4.

### Step 1: Define the variables based on the given ratio
Let:
- The number of Rs. 1 coins = 2x
- The number of Rs. 50 coins = 3x
- The number of Rs. 25 coins = 4x

### Step 2: Calculate the total value of each type of coin
Now, we calculate the total value contributed by each type of coin:
- Value from Rs. 1 coins = 2x * 1 = 2x
- Value from Rs. 50 coins = 3x * 0.50 = 1.5x
- Value from Rs. 25 coins = 4x * 0.25 = x

### Step 3: Set up the equation for the total value
The total value of all the coins is given as Rs. 180. Therefore, we can set up the equation:
\[ 2x + 1.5x + x = 180 \]

### Step 4: Simplify the equation
Combine like terms:
\[ 4.5x = 180 \]

### Step 5: Solve for x
To find the value of x, divide both sides by 4.5:
\[ x = \frac{180}{4.5} \]
\[ x = 40 \]

### Step 6: Find the number of 50 paise coins
Now, we can find the number of Rs. 50 coins:
\[ \text{Number of Rs. 50 coins} = 3x = 3 \times 40 = 120 \]

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

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