A person earn two rupees on the first day. If he earns double evey next day. What will be his earning at the `11^(th)` day-

Options

A. 1976
B. 2056
C. 1850
D. 2048

Answer

To solve the problem of how much a person earns on the 11th day if he starts with 2 rupees on the first day and doubles his earnings every subsequent day, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Earnings Pattern**:
- The person earns 2 rupees on the first day.
- Each subsequent day, he earns double the amount of the previous day.

2. **Calculate Earnings for Each Day**:
- Day 1: 2 rupees
- Day 2: 2 * 2 = 4 rupees
- Day 3: 4 * 2 = 8 rupees
- Day 4: 8 * 2 = 16 rupees
- Day 5: 16 * 2 = 32 rupees
- Day 6: 32 * 2 = 64 rupees
- Day 7: 64 * 2 = 128 rupees
- Day 8: 128 * 2 = 256 rupees
- Day 9: 256 * 2 = 512 rupees
- Day 10: 512 * 2 = 1024 rupees
- Day 11: 1024 * 2 = 2048 rupees

3. **Generalize the Earnings**:
- The earnings on day \( n \) can be expressed as:
\[ \text{Earnings on day } n = 2 \times 2^{(n-1)} = 2^n \]
- Therefore, for the 11th day:
\[ \text{Earnings on day 11} = 2^{11} = 2048 \text{ rupees} \]

### Final Answer:
The earnings on the 11th day will be **2048 rupees**.

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