Manu's piggy bank contains Rs. 221 in the form of 50 paise, Rs. 1 and Rs. 2 coins in the ratio of 4 :3:6. What is the number of 50 paise coins in the piggy bank?

Options

A. 52
B. 13
C. 104
D. 26

Answer

To solve the problem, we need to find the number of 50 paise coins in Manu's piggy bank, given that the coins are in the ratio of 4:3:6 for 50 paise, Rs. 1, and Rs. 2 coins, respectively.

### Step-by-Step Solution:

1. **Understand the Ratios**:
The coins are in the ratio of 4:3:6. This means for every 4 coins of 50 paise, there are 3 coins of Rs. 1, and 6 coins of Rs. 2.

2. **Assign Variables**:
Let the number of 50 paise coins be \(4x\), the number of Rs. 1 coins be \(3x\), and the number of Rs. 2 coins be \(6x\), where \(x\) is a common multiplier.

3. **Calculate the Total Value of Each Coin Type**:
- The value of 50 paise coins: \(4x \times 0.50 = 2x\) (since 50 paise = 0.50 Rs)
- The value of Rs. 1 coins: \(3x \times 1 = 3x\)
- The value of Rs. 2 coins: \(6x \times 2 = 12x\)

4. **Calculate the Total Value**:
The total value of all coins combined is:
\[ 2x + 3x + 12x = 17x \]

5. **Set Up the Equation**:
We know that the total value of the coins is Rs. 221. Therefore, we can set up the equation:
\[ 17x = 221 \]

6. **Solve for \(x\)**:
To find \(x\), divide both sides of the equation by 17:
\[ x = \frac{221}{17} = 13 \]

7. **Calculate the Number of 50 Paise Coins**:
Now, substitute \(x\) back to find the number of 50 paise coins:
\[ \text{Number of 50 paise coins} = 4x = 4 \times 13 = 52 \]

### Final Answer:
The number of 50 paise coins in the piggy bank is **52**.

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