Question : The red blood cells in a blood sample grow by 10% per hour in the first two hours, decrease by 10% in the next one hour, remain constant in the next one hour and again increase by 5% per hour in the next two hours. If the original count of the red blood cells in the sample is 40000, find the approximate red blood cell count at the end of 6 hours.
Option 1: 40,000
Option 2: 45,025
Option 3: 48,025
Option 4: 50,025
Correct Answer: 48,025
Solution :
The initial count of RBCs = 40,000
As we know, $x$ becomes $\frac{x(100+y)}{100}$ after increase of $y$% and $x$ becomes $\frac{x(100-y)}{100}$ after decrease of $y$%.
According to the question,
RBC count after 6 hours $= 40000 ×\frac{(100+10)}{100}×\frac{(100+10)}{100}×\frac{(100-10)}{100}×\frac{(100+5)}{100}×\frac{(100+5)}{100}$
$\therefore$ Approximate red blood cells count after 6 hours $= 40000 × 1.1 × 1.1 x 0.9 × 1.05 × 1.05 = 48024.9\approx48025$
Hence, the correct answer is 48,025.
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