The red blood cells in a blood sample grows by `10%` per hour in first two hours, decreases by `10%` in next one hour, remains constant in next one hour and again increases by `5%` per hour in next two hours. If the original count of the red blood cells in the sample is `40000`, find the approximated red blood cell count at the end of 6 hours.

Options

A. `40000`
B. `45025`
C. `48025`
D. `50025`

Answer

To solve the problem of calculating the red blood cell (RBC) count after 6 hours, we will follow the changes in the RBC count step by step based on the percentage increases and decreases provided in the question.

### Step-by-Step Solution:

1. **Initial Count**:
The original count of red blood cells is given as 40,000.

2. **First Two Hours (Increase by 10% each hour)**:
- After the first hour:
\[ \text{New Count} = \text{Original Count} + 10\% \text{ of Original Count} \]
\[ = 40000 + (0.10 \times 40000) = 40000 + 4000 = 44000 \]
- After the second hour:
\[ \text{New Count} = 44000 + 10\% \text{ of 44000} \]
\[ = 44000 + (0.10 \times 44000) = 44000 + 4400 = 48400 \]

3. **Third Hour (Decrease by 10%)**:
- After the third hour:
\[ \text{New Count} = 48400 - 10\% \text{ of 48400} \]
\[ = 48400 - (0.10 \times 48400) = 48400 - 4840 = 43560 \]

4. **Fourth Hour (Constant)**:
- After the fourth hour, the count remains the same:
\[ \text{New Count} = 43560 \]

5. **Fifth and Sixth Hours (Increase by 5% each hour)**:
- After the fifth hour:
\[ \text{New Count} = 43560 + 5\% \text{ of 43560} \]
\[ = 43560 + (0.05 \times 43560) = 43560 + 2178 = 45738 \]
- After the sixth hour:
\[ \text{New Count} = 45738 + 5\% \text{ of 45738} \]
\[ = 45738 + (0.05 \times 45738) = 45738 + 2286.9 \approx 48025 \]

### Final Count:
The approximated red blood cell count at the end of 6 hours is approximately **48,025**.

---