In a bag, the ratio of Rs. 1, Rs. 2 and Rs. 5 coins is 2 : 3 : 8 and the total amount in the bag is Rs.432. Then find the number of 2 rupees coins.

Options

A. 27
B. 18
C. 24
D. 15

Answer

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

### Step 1: Understand the Ratio
The ratio of Rs. 1, Rs. 2, and Rs. 5 coins is given as 2 : 3 : 8. This means for every 2 Rs. 1 coins, there are 3 Rs. 2 coins and 8 Rs. 5 coins.

### Step 2: Assign Variables
Let's assign a variable \( x \) to represent the common multiple of the ratio. Therefore:
- Number of Rs. 1 coins = \( 2x \)
- Number of Rs. 2 coins = \( 3x \)
- Number of Rs. 5 coins = \( 8x \)

### Step 3: Calculate the Total Value of Each Type of Coin
Now, we can calculate the total value contributed by each type of coin:
- Value from Rs. 1 coins = \( 2x \times 1 = 2x \)
- Value from Rs. 2 coins = \( 3x \times 2 = 6x \)
- Value from Rs. 5 coins = \( 8x \times 5 = 40x \)

### Step 4: Set Up the Total Value Equation
The total value of all coins is given as Rs. 432. Therefore, we can set up the equation:
\[ 2x + 6x + 40x = 432 \]

### Step 5: Combine Like Terms
Combine the terms on the left side:
\[ 48x = 432 \]

### Step 6: Solve for \( x \)
Now, divide both sides by 48 to find \( x \):
\[ x = \frac{432}{48} = 9 \]

### Step 7: Find the Number of Rs. 2 Coins
Now that we have \( x \), we can find the number of Rs. 2 coins:
\[ \text{Number of Rs. 2 coins} = 3x = 3 \times 9 = 27 \]

### Conclusion
The number of Rs. 2 coins in the bag is **27**.

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