The empty weight of a jar is 20% of its weight when it is completely filled with water. If some water is taken out of jar such that the current weight of the jar is 40% of its weight when it is completely filled with water. What percentage of water is taken out of jar.

1) 70%

2) 60%

3) 85%

4) 50%

5) None of these

Let's denote the weight of the jar when it is completely filled with water as \( W \).

### Step 1: Determine the weight of the empty jar
The empty weight of the jar is 20% of the weight when it is completely filled with water. So, the weight of the empty jar is:
\[
0.2W
\]

### Step 2: Determine the current weight of the jar
The current weight of the jar is given as 40% of the weight when it is completely filled with water. Therefore, the current weight is:
\[
0.4W
\]

### Step 3: Calculate the weight of the water currently in the jar
The weight of the water currently in the jar is the difference between the current weight and the empty weight:
\[
\text{Weight of current water} = 0.4W - 0.2W = 0.2W
\]

### Step 4: Calculate the weight of the water when the jar is full
The weight of the water when the jar is completely filled with water is:
\[
\text{Weight of full water} = W - 0.2W = 0.8W
\]

### Step 5: Calculate the percentage of water taken out
Let \( x \) be the percentage of water taken out. The amount of water remaining is \( 0.2W \), and originally it was \( 0.8W \). Therefore:
\[
\text{Percentage of water taken out} = \frac{0.8W - 0.2W}{0.8W} \times 100\% = \frac{0.6W}{0.8W} \times 100\% = 75\%
\]

Since 75% isn't an option provided, the correct answer is:
\[
\boxed{5) \text{None of these}}
\]

Would you like to explore the details further or have any questions?

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Here are some related questions:

1. What would the answer be if the jar were initially 50% full?
2. How does the percentage change if the jar's empty weight is 30% of its full weight?
3. If the jar's empty weight is increased by 10%, how would the problem change?
4. What if the current weight is 60% of the full jar instead of 40%?
5. How can we calculate the weight of the water remaining if 50% is removed?
6. If the jar's weight doubles when full, how would the percentage removed change?
7. How would this problem change if the jar was filled with another liquid with a different density?
8. Can you create a similar problem with a different

Understand how to calculate the percentage of water removed from a jar based on its weight when full and current weight. Explore step-by-step solutions and variations of this problem.

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