Question

From a 64-liter container of pure spirit, 8 liters are removed and replaced by water. This operation is performed a total of three times. What is the final quantity of spirit remaining in the container?

• A. 34.34 liters
• B. 36.45 litres
• C. 38.62 litres
• D. 42.88 litres

Answer 1

Answer:

D. 42.88 litres

Use the replacement formula:

$\text{Final quantity of spirit}$
$= V\left(1-\frac{x}{V}\right)^n$

Where:

• (V = 64) L

• (x = 8) L removed each time

• (n = 3)

So,

$64\left(1-\frac{8}{64}\right)^3$
$=64\left(\frac{56}{64}\right)^3$
$=64\left(\frac{7}{8}\right)^3$
$=64 \times \frac{343}{512}$
$=\frac{343}{8}$
$=42.875$

So, the final quantity of spirit remaining is:

$\boxed{42.88 \text{ liters}}$