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Several litre of Acid were drawn off a 54-litre vessel full of Acid and an equal amount of water added. Again the same volume of the mixture was drawn off and replaced by water as a result the vessel contained 24 litres of pure acid. How much of the Acid was drawn off initially?
- a)12 liters
- b)16 liters
- c)18 liters
- d)24 litres
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Several litre of Acid were drawn off a 54-litre vessel full of Acid an...
Lets initialy x liter of water drawn off
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Several litre of Acid were drawn off a 54-litre vessel full of Acid an...
Given:
- A 54-litre vessel full of acid and water mixture
- Several litres of acid were drawn off and an equal amount of water was added
- Again, the same volume of the mixture was drawn off and replaced by water
- The vessel contained 24 litres of pure acid
To find:
- How much of the acid was drawn off initially
Solution:
Let's assume that initially, x litres of acid were drawn off.
After drawing off x litres of acid, the vessel contains:
- Acid = (54 - x) litres
- Water = (54 - x) litres
Now, an equal amount of water is added to the vessel. So the vessel contains:
- Acid = (54 - x) litres
- Water = (54 - x) + x = 54 litres
Next, the same volume of the mixture is drawn off and replaced by water. So, the amount of acid in the vessel will be reduced by x litres again.
After this process, the vessel contains:
- Acid = (54 - x) - x = 54 - 2x litres
- Water = 54 litres
According to the question, the vessel contains 24 litres of pure acid after this process. So, we can write the following equation:
24 = (54 - 2x) / 2
Solving this equation, we get:
x = 18
Therefore, initially, 18 litres of acid were drawn off from the vessel.
Hence, option (c) is the correct answer.
- A 54-litre vessel full of acid and water mixture
- Several litres of acid were drawn off and an equal amount of water was added
- Again, the same volume of the mixture was drawn off and replaced by water
- The vessel contained 24 litres of pure acid
To find:
- How much of the acid was drawn off initially
Solution:
Let's assume that initially, x litres of acid were drawn off.
After drawing off x litres of acid, the vessel contains:
- Acid = (54 - x) litres
- Water = (54 - x) litres
Now, an equal amount of water is added to the vessel. So the vessel contains:
- Acid = (54 - x) litres
- Water = (54 - x) + x = 54 litres
Next, the same volume of the mixture is drawn off and replaced by water. So, the amount of acid in the vessel will be reduced by x litres again.
After this process, the vessel contains:
- Acid = (54 - x) - x = 54 - 2x litres
- Water = 54 litres
According to the question, the vessel contains 24 litres of pure acid after this process. So, we can write the following equation:
24 = (54 - 2x) / 2
Solving this equation, we get:
x = 18
Therefore, initially, 18 litres of acid were drawn off from the vessel.
Hence, option (c) is the correct answer.
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Several litre of Acid were drawn off a 54-litre vessel full of Acid and an equal amount of water added. Again the same volume of the mixture was drawn off and replaced by water as a result the vessel contained 24 litres of pure acid. How much of the Acid was drawn off initially?a)12 litersb)16 litersc)18 litersd)24 litrese)None of theseCorrect answer is option 'C'. Can you explain this answer?
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