Question

A jug was full of juice. A person draws out \( \frac{1}{6} \) of the juice from the jug and replaces it with water. He repeated this process 3 times and thus there was only 1250 ml of juice left in the jug. What was the initial quantity of juice in the jug?

• A. 2.775 L
• B. 2.565 L
• C. 2.330 L
• D. 2.160 L

Hint:

When liquid is replaced repeatedly, use this formula:
\[ \text{Final quantity} = \text{Initial quantity} \times \left(1 - \frac{x}{V}\right)^n \] where \( x \) is the amount replaced each time, and \( n \) is the number of repetitions.

Answer 1

The Correct Option is D

Step 1: Use the concept of successive replacement.
Each time, \( \frac{1}{6} \) of the juice is removed and replaced with water. So, \( \frac{5}{6} \) of the juice remains after each operation. Step 2: Use the general formula for remaining quantity of original liquid: \[ \text{Final amount of juice} = \text{Initial quantity} \times \left( \frac{5}{6} \right)^n \] where \( n = 3 \) (process repeated 3 times). Step 3: Let initial quantity of juice = \( V \) ml.
We are given: \[ \left( \frac{5}{6} \right)^3 = \frac{125}{216}, \quad \text{and final juice left} = 1250 \, \text{ml} \] So, \[ 1250 = V \cdot \frac{125}{216} \] Step 4: Solve for \( V \). \[ V = \frac{1250 \times 216}{125} = \frac{270000}{125} = 2160 \, \text{ml} \] Step 5: Convert to liters. \[ 2160 \, \text{ml} = 2.160 \, \text{liters} \]