Mr. Mohan has `256rs` in the form of `1rs` and `2rs` coins. If the number of `2rs` coins are three more than twice the number of `1rs` coins find the total value of `2rs` coins

Answer

To solve the problem step by step, we will define the variables, set up the equations based on the information given, and then solve for the unknowns.

### Step 1: Define the Variables
Let:
- \( x \) = number of 1 rupee coins
- \( y \) = number of 2 rupee coins

### Step 2: Set Up the Equations
From the problem, we know:
1. The total amount of money is 256 rupees:
\[ x + 2y = 256 \quad \text{(Equation 1)} \]
2. The number of 2 rupee coins is three more than twice the number of 1 rupee coins:
\[ y = 2x + 3 \quad \text{(Equation 2)} \]

### Step 3: Substitute Equation 2 into Equation 1
We can substitute the expression for \( y \) from Equation 2 into Equation 1:
\[ x + 2(2x + 3) = 256 \]
Expanding this gives:
\[ x + 4x + 6 = 256 \]
Combining like terms:
\[ 5x + 6 = 256 \]

### Step 4: Solve for \( x \)
Now, we will isolate \( x \):
\[ 5x = 256 - 6 \]
\[ 5x = 250 \]
\[ x = \frac{250}{5} = 50 \]

### Step 5: Solve for \( y \)
Now that we have \( x \), we can find \( y \) using Equation 2:
\[ y = 2(50) + 3 \]
\[ y = 100 + 3 = 103 \]

### Step 6: Calculate the Total Value of 2 Rupee Coins
Now we can find the total value of the 2 rupee coins:
\[ \text{Total value of 2 rupee coins} = 2y = 2 \times 103 = 206 \text{ rupees} \]

### Final Answer
The total value of the 2 rupee coins is **206 rupees**.

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