A sum of Rs.110 is in the form of Rs.2, Rs.1 and 50 paise coins in the ratio of 1 : 2 : 3. respectively. How many 50 paise coins are there?

Options

A. 20
B. 60
C. 40
D. 80

Answer

To solve the problem step by step, we will follow the given information and the ratios provided.

### Step 1: Understand the Ratios
We are given that the coins are in the ratio of Rs. 2 : Rs. 1 : 50 paise = 1 : 2 : 3. This means for every 1 coin of Rs. 2, there are 2 coins of Rs. 1 and 3 coins of 50 paise.

### Step 2: Assign Variables
Let the number of Rs. 2 coins be \( x \).
Then, the number of Rs. 1 coins will be \( 2x \) (since the ratio is 2).
The number of 50 paise coins will be \( 3x \) (since the ratio is 3).

### Step 3: Calculate the Total Value of Each Coin Type
- The total value of Rs. 2 coins = \( 2 \times x = 2x \) rupees.
- The total value of Rs. 1 coins = \( 1 \times 2x = 2x \) rupees.
- The total value of 50 paise coins = \( 0.5 \times 3x = \frac{3x}{2} \) rupees.

### Step 4: Set Up the Equation
According to the problem, the total amount of money is Rs. 110. Therefore, we can set up the equation:
\[ 2x + 2x + \frac{3x}{2} = 110 \]

### Step 5: Simplify the Equation
Combine the terms on the left side:
\[ 4x + \frac{3x}{2} = 110 \]
To eliminate the fraction, multiply the entire equation by 2:
\[ 2(4x) + 3x = 220 \]
This simplifies to:
\[ 8x + 3x = 220 \]
\[ 11x = 220 \]

### Step 6: Solve for \( x \)
Now, divide both sides by 11:
\[ x = \frac{220}{11} = 20 \]

### Step 7: Find the Number of 50 Paise Coins
We know that the number of 50 paise coins is \( 3x \):
\[ 3x = 3 \times 20 = 60 \]

### Conclusion
Thus, the number of 50 paise coins is **60**.

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