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Question
A vessel contains water and acid in the ratio 16: 5. 31.5 litres of the mixture is taken out from the vessel and 2.5 litres of acid and 4 litres of water is added to the mixture. If the resultant mixture contains 25% acid, what was the initial quantity of mixture in the vessel before replacement?
A vessel contains water and acid in the ratio 16: 5. 31.5 litres of the mixture is taken out from the vessel and 2.5 litres of acid and 4 litres of water is added to the mixture. If the resultant mixture contains 25% acid, what was the initial quantity of mixture in the vessel before replacement?
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Solution
The correct option is B 105 L
Initial quantity of mixture = 16x+5x = 21x
After removing 31.5 litres = 16x -24: 5x -7.5
After adding back acid and water = 16x -20: 5x -5
Water accounts for 25% of total ⇒3(5x−5)=16x−20⇒x=5
Initial quantity before removing from it =21×5=105 litres
Initial quantity of mixture = 16x+5x = 21x
After removing 31.5 litres = 16x -24: 5x -7.5
After adding back acid and water = 16x -20: 5x -5
Water accounts for 25% of total ⇒3(5x−5)=16x−20⇒x=5
Initial quantity before removing from it =21×5=105 litres
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