Question

A container contains 100 litres of apple juice. From this container, 10 litres of apple juice was taken out and replaced by water. This process was further repeated twice. How much apple juice is left in the container?

• A. \( 72.9 \) litres
• B. \( 75.2 \) litres
• C. \( 63.2 \) litres
• D. \( 54.6 \) litres

Hint:

Always identify the total number of cycles carefully. "Repeated twice" means the process happened a total of 3 times.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a standard problem of successive dilution. The remaining amount of the original substance is calculated using the formula: \( Remaining = V(1 - \frac{r}{V})^n \).

Step 2: Key Formula or Approach:
Here, \( V = 100 \) (initial volume), \( r = 10 \) (volume removed), and \( n = 3 \) (the process was performed once and repeated twice).

Step 3: Detailed Explanation:
\[ Remaining = 100 \left(1 - \frac{10}{100}\right)^3 \]
\[ Remaining = 100 \left(1 - 0.1\right)^3 = 100 \times (0.9)^3 \]
\[ Remaining = 100 \times 0.729 = 72.9 \text{ litres} \]

Step 4: Final Answer:
The amount of apple juice left in the container is \( 72.9 \) litres.