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Several litres 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 litres
- b)16 litres
- c)18 litres
- d)24 litres
Correct answer is option 'C'. Can you explain this answer?
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Several litres of acid were drawn off a 54-litre vessel full of acid a...
If a container contains x units of liquid and y units of liquid is taken out. If this operation is repeated n times. The final quantity of the liquid in the container is
where x = amount of acid initially drawn off
where x = amount of acid initially drawn off
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Several litres of acid were drawn off a 54-litre vessel full of acid a...
Given:
- 54L vessel filled with acid
- Several litres of acid were drawn off
- An equal amount of water was added
- Same volume of the mixture was drawn off and replaced by water
- Result: vessel contained 24L of pure acid
To find: Initial amount of acid drawn off
Solution:
Let's assume that x litres of acid were drawn off initially.
Step 1: After the first step (drawing off x litres of acid and adding x litres of water), the vessel will contain:
- (54-x) litres of the original mixture (acid + water)
- x litres of water
- The concentration of acid in the mixture will be: (54-x-x)/54 = (54-2x)/54
Step 2: After the second step (drawing off the same volume of mixture and replacing with water), the vessel will contain:
- (54-x-x) = (54-2x) litres of the original mixture (acid + water)
- x litres of water
- The concentration of acid in the mixture will be: (54-2x-x)/54 = (54-3x)/54
Step 3: After the second step, the vessel contains 24L of pure acid. This means that the remaining (54-3x) litres of mixture contains no acid. Therefore, we can write the equation:
(54-3x)/(54-x-x) = 0
Simplifying this equation, we get:
54 - 3x = 0
x = 18
Therefore, the initial amount of acid drawn off was 18 litres.
Answer: Option (c) 18 litres.
- 54L vessel filled with acid
- Several litres of acid were drawn off
- An equal amount of water was added
- Same volume of the mixture was drawn off and replaced by water
- Result: vessel contained 24L of pure acid
To find: Initial amount of acid drawn off
Solution:
Let's assume that x litres of acid were drawn off initially.
Step 1: After the first step (drawing off x litres of acid and adding x litres of water), the vessel will contain:
- (54-x) litres of the original mixture (acid + water)
- x litres of water
- The concentration of acid in the mixture will be: (54-x-x)/54 = (54-2x)/54
Step 2: After the second step (drawing off the same volume of mixture and replacing with water), the vessel will contain:
- (54-x-x) = (54-2x) litres of the original mixture (acid + water)
- x litres of water
- The concentration of acid in the mixture will be: (54-2x-x)/54 = (54-3x)/54
Step 3: After the second step, the vessel contains 24L of pure acid. This means that the remaining (54-3x) litres of mixture contains no acid. Therefore, we can write the equation:
(54-3x)/(54-x-x) = 0
Simplifying this equation, we get:
54 - 3x = 0
x = 18
Therefore, the initial amount of acid drawn off was 18 litres.
Answer: Option (c) 18 litres.
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Several litres 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 litresb)16 litresc)18 litresd)24 litresCorrect answer is option 'C'. Can you explain this answer?
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