Aruna has only Rs. `1` and Rs. `2` coins with her. If the total number of coins that she has is `50` and the amount of money with her is Rs. `75`, then the number of Rs. `1` and Rs. `2` coins are, respectively

Options

A. `35` and `15`
B. `35` and `20`
C. `15` and `35`
D. `25` and `25`

Explanation

To solve the problem step by step, we can set up a system of equations based on the information given.

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

### Step 2: Set Up the Equations
From the problem, we know:
1. The total number of coins is 50:
\[ x + y = 50 \quad \text{(Equation 1)} \]
2. The total value of the coins is Rs. 75:
\[ 1x + 2y = 75 \quad \text{(Equation 2)} \]

### Step 3: Solve Equation 1 for One Variable
We can solve Equation 1 for \( y \):
\[ y = 50 - x \quad \text{(Substituting for } y \text{)} \]

### Step 4: Substitute into Equation 2
Now, substitute \( y \) in Equation 2:
\[ x + 2(50 - x) = 75 \]

### Step 5: Simplify the Equation
Distributing the 2:
\[ x + 100 - 2x = 75 \]
Combine like terms:
\[ - x + 100 = 75 \]

### Step 6: Solve for \( x \)
Subtract 100 from both sides:
\[ -x = 75 - 100 \]
\[ -x = -25 \]
Multiply by -1:
\[ x = 25 \]

### Step 7: Find \( y \)
Now substitute \( x \) back into the equation for \( y \):
\[ y = 50 - x = 50 - 25 = 25 \]

### Conclusion
Thus, the number of Rs. 1 coins is \( 25 \) and the number of Rs. 2 coins is \( 25 \).

### Final Answer
The number of Rs. 1 and Rs. 2 coins are, respectively, \( 25 \) and \( 25 \).

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