A woman has Rs 550 in her purse. She has only Rs 50 and Rs 10 note which are 23 in total, then Rs 10 notes in her purse are

Options

A. 15
B. 8
C. 20
D. 11

Explanation

To solve the problem step by step, we need to find out how many Rs 10 notes the woman has in her purse.

### Step 1: Define Variables
Let:
- \( x \) = number of Rs 50 notes
- \( y \) = number of Rs 10 notes

### Step 2: Set Up the Equations
From the problem, we know:
1. The total number of notes is 23:
\[ x + y = 23 \quad \text{(Equation 1)} \]
2. The total amount of money is Rs 550:
\[ 50x + 10y = 550 \quad \text{(Equation 2)} \]

### Step 3: Simplify Equation 2
To make calculations easier, we can divide the entire Equation 2 by 10:
\[ 5x + y = 55 \quad \text{(Equation 3)} \]

### Step 4: Subtract Equation 1 from Equation 3
Now, we will subtract Equation 1 from Equation 3:
\[ (5x + y) - (x + y) = 55 - 23 \]
This simplifies to:
\[ 5x + y - x - y = 32 \]
Which further simplifies to:
\[ 4x = 32 \]

### Step 5: Solve for \( x \)
Now, divide both sides by 4:
\[ x = \frac{32}{4} = 8 \]
So, the number of Rs 50 notes \( x \) is 8.

### Step 6: Substitute \( x \) back into Equation 1
Now, we can find \( y \) by substituting \( x \) back into Equation 1:
\[ 8 + y = 23 \]
Subtract 8 from both sides:
\[ y = 23 - 8 = 15 \]

### Conclusion
The number of Rs 10 notes \( y \) is 15.

### Final Answer
The woman has **15 Rs 10 notes** in her purse.

---