Rs 180 contained in a box consists of Rs 1,50 paise and 25 paise coins in the ratio `5:6:8` .What is the number of 50 paise coins ?

Answer

To solve the problem, we need to find the number of 50 paise coins when Rs 180 is divided into Rs 1, 50 paise, and 25 paise coins in the ratio of 5:6:8.

### Step 1: Understand the Ratio
The ratio of Rs 1, 50 paise, and 25 paise coins is given as 5:6:8. This means:
- For every 5 parts of Rs 1 coins, there are 6 parts of 50 paise coins and 8 parts of 25 paise coins.

### Step 2: Assign Variables
Let the common multiple be \( x \). Therefore, we can express the number of coins as:
- Rs 1 coins = \( 5x \)
- 50 paise coins = \( 6x \)
- 25 paise coins = \( 8x \)

### Step 3: Calculate the Total Value
Now, we need to calculate the total value contributed by each type of coin:
- Value from Rs 1 coins = \( 5x \times 1 = 5x \) rupees
- Value from 50 paise coins = \( 6x \times 0.5 = 3x \) rupees
- Value from 25 paise coins = \( 8x \times 0.25 = 2x \) rupees

### Step 4: Set Up the Equation
The total value of all coins must equal Rs 180:
\[ 5x + 3x + 2x = 180 \]

### Step 5: Simplify the Equation
Combine the terms:
\[ 10x = 180 \]

### Step 6: Solve for \( x \)
Now, divide both sides by 10:
\[ x = \frac{180}{10} = 18 \]

### Step 7: Find the Number of 50 Paise Coins
Now, substitute \( x \) back to find the number of 50 paise coins:
\[ \text{Number of 50 paise coins} = 6x = 6 \times 18 = 108 \]

### Final Answer
The number of 50 paise coins is **108**.

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