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The problem is about determining the number of coins Rakshita has, where she has 1-rupee and 2-rupee coins, given two conditions:

1. The total number of coins is 50.
2. The total value of the coins is ₹75.

Let's define:
- \( x \) as the number of 1-rupee coins.
- \( y \) as the number of 2-rupee coins.

We can set up the following system of equations based on the information given:

1. The total number of coins:
   \[
   x + y = 50
   \]
   
2. The total value of the coins:
   \[
   1x + 2y = 75
   \]

### Solving the system:

1. From the first equation, solve for \( x \):
   \[
   x = 50 - y
   \]

2. Substitute this into the second equation:
   \[
   1(50 - y) + 2y = 75
   \]
   Simplify:
   \[
   50 - y + 2y = 75
   \]
   \[
   50 + y = 75
   \]
   \[
   y = 75 - 50 = 25
   \]

3. Now, substitute \( y = 25 \) back into the first equation:
   \[
   x + 25 = 50
   \]
   \[
   x = 50 - 25 = 25
   \]

Thus, Rakshita has **25 coins of 1 rupee** and **25 coins of 2 rupees**.

### Answer:
The correct answer is **Option D: 25 and 25**.

Would you like further details or have any questions? Here are some related questions to expand your understanding:

1. How do you solve a system of linear equations using substitution?
2. What is the difference between 1-rupee and 2-rupee coin value equations?
3. Can you solve similar problems using the elimination method?
4. How do different methods of solving linear equations compare?
5. What other types of problems can be solved using systems of equations?

**Tip:** Always simplify equations step-by-step to avoid errors in substitution or calculation!

रक्षिता के पास केवल 1 व 2 रूपये के सिक्के है। यदि उसके पास सिक्को की कुल संख्या 50 है तथा कुल रूपये 75 हो तो 1 व 2 रूपये के सिक्के क्रमशः कितने हैं?

Learn how to solve a system of linear equations to determine the number of 1-rupee and 2-rupee coins Rakshita has. This problem involves a total of 50 coins amounting to ₹75, and uses substitution methods to find the solution. Suitable for Grades 6-8.

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