After spending `69%` of her money, a lady is left with `Rs. 93` . How much had she at first ?

Options

A. Rs. `300`
B. Rs. `400`
C. Rs. `75`
D. Rs. `150`

Answer

To solve the problem step by step, we can follow these calculations:

1. **Understanding the Problem**:
- The lady spends 69% of her total money and is left with Rs. 93.
- Let the total amount of money she had initially be represented as \( x \).

2. **Calculating the Amount Spent**:
- If she spends 69% of her money, then the amount spent can be expressed as:
\[ \text{Amount spent} = 69\% \text{ of } x = \frac{69}{100} \times x = \frac{69x}{100} \]

3. **Calculating the Amount Left**:
- The amount left after spending is given as Rs. 93. This can be expressed as:
\[ \text{Amount left} = x - \text{Amount spent} \]
- Substituting the amount spent into the equation:
\[ 93 = x - \frac{69x}{100} \]

4. **Simplifying the Equation**:
- To simplify \( x - \frac{69x}{100} \), we can express \( x \) as \( \frac{100x}{100} \):
\[ 93 = \frac{100x}{100} - \frac{69x}{100} \]
- This simplifies to:
\[ 93 = \frac{100x - 69x}{100} = \frac{31x}{100} \]

5. **Solving for \( x \)**:
- To isolate \( x \), multiply both sides by 100:
\[ 93 \times 100 = 31x \]
\[ 9300 = 31x \]
- Now, divide both sides by 31:
\[ x = \frac{9300}{31} \]
- Performing the division:
\[ x = 300 \]

6. **Conclusion**:
- The total amount of money the lady had initially is Rs. 300.