Question

A container has 50 litres of juice in it. 5 litres of juice is taken out and is replaced by 5 litres of water. This process is repeated 4 more times. Determine the quantity of juice in the container after final replacement.
[Use \( (0.9)^5 = 0.59049 \)]

Hint:

For problems involving repeated replacement, use \( {Remaining Quantity} = {Initial Quantity} \times ( {Fraction Remaining})^n \), where \( n \) is the number of replacements.

Answer 1

Step 1: The fraction of juice remaining after each replacement is \( \frac{50 - 5}{50} = 0.9 \).
Step 2: After 5 replacements, the quantity of juice remaining is: \[ {Quantity of Juice} = 50 \cdot (0.9)^5 = 50 \cdot 0.59049 = 29.5245 \, {litres}. \] Thus, the final quantity of juice is approximately \( 29.52 \, {litres} \).