Sunita has some Rs. 50 and Rs. 100 notes amounting to a total of Rs. 15,500. If the total number of notes is 200, then find how many notes of Rs. 50 and Rs. 100 each, she has.

Answer

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

### Step 1: Define the variables
Let:
- \( X \) = number of Rs. 50 notes
- \( Y \) = number of Rs. 100 notes

### Step 2: Set up the equations
From the problem, we know two things:
1. The total number of notes is 200.
2. The total amount of money is Rs. 15,500.

This gives us the following equations:
1. \( X + Y = 200 \) (Equation 1)
2. \( 50X + 100Y = 15500 \) (Equation 2)

### Step 3: Simplify Equation 2
We can simplify Equation 2 by dividing everything by 50:
\[ X + 2Y = 310 \quad (Equation 3) \]

### Step 4: Solve the system of equations
Now we have two equations:
1. \( X + Y = 200 \) (Equation 1)
2. \( X + 2Y = 310 \) (Equation 3)

We can subtract Equation 1 from Equation 3:
\[ (X + 2Y) - (X + Y) = 310 - 200 \]
This simplifies to:
\[ Y = 110 \]

### Step 5: Substitute back to find X
Now that we have \( Y \), we can substitute it back into Equation 1 to find \( X \):
\[ X + 110 = 200 \]
Subtracting 110 from both sides gives:
\[ X = 90 \]

### Step 6: Conclusion
Thus, the number of Rs. 50 notes (X) is 90, and the number of Rs. 100 notes (Y) is 110.

### Final Answer:
- Number of Rs. 50 notes = 90
- Number of Rs. 100 notes = 110

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