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Some quantity of juice from a container of 60 litres of apple juice is replaced with mango juice. Same quantity of the mixture is drawn again and is replaced by equal quantity of mango juice. After this, quantity of apple juice left in the container is (4/9)th of the initial quantity. What quantity of the liquid is taken out from the container both time (in litres)? 
  • a)
    25
  • b)
    20
  • c)
    18
  • d)
     15
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Some quantity of juice from a container of 60 litres of apple juice is...
Let the qunatity drawn from the container both times be x.
Solving this we get, x = 20 litres
Hence, option 2.
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Most Upvoted Answer
Some quantity of juice from a container of 60 litres of apple juice is...
Given:

- Initial quantity of apple juice in the container = 60 litres
- Some quantity of apple juice is replaced with mango juice
- Same quantity of the mixture is drawn again and is replaced by equal quantity of mango juice
- Quantity of apple juice left in the container after the process = (4/9) * 60 = 26.67 litres

To find:

- Quantity of the liquid taken out from the container both times

Solution:

Let's assume that x litres of the mixture is replaced with mango juice both times.

After the first replacement, the quantity of apple juice left in the container = 60 - x litres

Now, x litres of the mixture is drawn from the container and replaced with mango juice.

So, the quantity of apple juice left in the container after the second replacement = (60 - x) * (1 - x/60)

According to the given information, this quantity is equal to (4/9) * 60 = 26.67 litres.

Therefore, we can write the equation as:

(60 - x) * (1 - x/60) = 26.67

Simplifying this equation, we get:

x^2 - 40x + 800 = 0

Solving this quadratic equation gives us two solutions:

x = 20 or x = 40

Since x cannot be greater than 60 (the initial quantity of the container), the only possible solution is x = 20.

Therefore, the quantity of the liquid taken out from the container both times is 20 litres.

Hence, the correct answer is option (B) 20.
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Community Answer
Some quantity of juice from a container of 60 litres of apple juice is...
Let x amount be replaced. At first x litre of apple juice is taken away. The mixture now contains x mango and 60 - x apple juice. If we remove x litre from this mixture it will contain (60-x)*x/60 apple juice. So total apple juice removed is x + ((60-x)*x)/60 =(5/9)*60(removed apple juice) by trail and error answer is 20 Option B
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Some quantity of juice from a container of 60 litres of apple juice is replacedwith mango juice. Same quantity of the mixture is drawn again and is replaced by equal quantity of mango juice. After this, quantity of apple juice left in the container is (4/9)th of the initial quantity. What quantity of the liquid is taken out from the container both time (in litres)?a)25b)20c)18d)15Correct answer is option 'B'. Can you explain this answer?
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