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, we will define the variables and set up equations based on the information given.

### Step-by-step Solution:

1. **Define the Variables**:
Let \( X \) be the number of Rs. 1 coins and \( Y \) be the number of Rs. 2 coins.

2. **Set Up the Equations**:
From the problem statement, we have two pieces of information:
- The total number of coins is 50.
- The total amount of money is Rs. 75.

This gives us the following equations:
- Equation 1: \( X + Y = 50 \) (total number of coins)
- Equation 2: \( 1X + 2Y = 75 \) (total amount of money)

3. **Rearranging the Equations**:
We can express \( Y \) in terms of \( X \) using Equation 1:
\[ Y = 50 - X \]

4. **Substituting into the Second Equation**:
Now, substitute \( Y \) in Equation 2:
\[ X + 2(50 - X) = 75 \]
Simplifying this gives:
\[ X + 100 - 2X = 75 \]
\[ -X + 100 = 75 \]
\[ -X = 75 - 100 \]
\[ -X = -25 \]
\[ X = 25 \]

5. **Finding \( Y \)**:
Now that we have \( X \), we can find \( Y \):
\[ Y = 50 - X = 50 - 25 = 25 \]

6. **Conclusion**:
The number of Rs. 1 coins is \( X = 25 \) and the number of Rs. 2 coins is \( Y = 25 \).

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

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