Karan spent half of his pocket money to buy a pair of shoes. He spent half the remaining for a book. He also spent half the remaining to buy a study table. He was left with Rs. 350. With how much money he started his shopping?

Options

A. Rs. 4000
B. Rs. 3000
C. Rs. 2800
D. Rs. 1080

Answer

To find out how much money Karan started with, we can break down the problem step by step.

### Step-by-Step Solution:

1. **Let Karan's initial pocket money be \( X \)**.
- This is our starting point.

2. **Karan spent half of his pocket money on shoes**:
- Amount spent on shoes = \( \frac{X}{2} \)
- Remaining money after buying shoes = \( X - \frac{X}{2} = \frac{X}{2} \)

3. **Karan spent half of the remaining money on a book**:
- Amount spent on the book = \( \frac{1}{2} \times \frac{X}{2} = \frac{X}{4} \)
- Remaining money after buying the book = \( \frac{X}{2} - \frac{X}{4} = \frac{X}{4} \)

4. **Karan spent half of the remaining money on a study table**:
- Amount spent on the study table = \( \frac{1}{2} \times \frac{X}{4} = \frac{X}{8} \)
- Remaining money after buying the study table = \( \frac{X}{4} - \frac{X}{8} = \frac{X}{8} \)

5. **We know that Karan was left with Rs. 350**:
- So, we can set up the equation:
\[ \frac{X}{8} = 350 \]

6. **To find \( X \)**, multiply both sides of the equation by 8:
\[ X = 350 \times 8 \]
\[ X = 2800 \]

### Conclusion:
Karan started his shopping with **Rs. 2800**.

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