Question : A vessel contained a solution of acid and water, in which water was 64%. Four litres of the solution was taken out of the vessel and the same quantity of water was added. If the resulting solution contains 30% acid, the quantity (in litres) of the water in the solution, at the beginning of the vessel, was:
Option 1: 11.36
Option 2: 15.36
Option 3: 8.64
Option 4: 12.64
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Correct Answer: 15.36
Solution : Water in the solution = 64% Acid in the solution = 100% – 64% = 36% Acid in the new solution = 30% Water in the new solution = 100% – 30% = 70% Let the total solution be $100x$ Water = $64x$ Acid = $36x$ According to the question, $\frac{{64x - 4 × \frac{64}{100} + 4}}{36x - 4 × \frac{36}{100}} = \frac{7}{3}$ ⇒ $\frac{64x + 1.44}{36x - 1.44} = \frac{7}{3}$ ⇒ $192x + 4.32 = 252x - 10.08$ ⇒ $60x = 14.4$ ⇒ $x = 0.24$ Thus, $64x = 64 × 0.24= 15.36$ litres Hence, the correct answer is 15.36.
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Question : A mixture of acid and water contains 20% acid. When 10 litres of water is added to the mixture, then the percentage of acid becomes 15%. What is the original quantity of the mixture?
Option 1: 30 litres
Option 2: 25 litres
Option 3: 40 litres
Option 4: 35 litres
Question : A vessel contains 20 L of acid. 4 L of acid is taken out of the vessel and replaced by the same quantity of water. Next, 4 L of the mixture is withdrawn and again the vessel is filled with the same quantity of water. The ratio of the quantity of acid left in the vessel with the quantity of acid initially in the vessel is:
Option 1: 4 : 5
Option 2: 4 : 25
Option 3: 16 : 25
Option 4: 1 : 5
Question : A mixture contains milk and water in a ratio of 5 : 3, respectively. On adding 7 litres of water, the ratio of milk to water becomes 1 : 2. Find the quantity of milk in the mixture.
Option 1: 7 litres
Option 2: 10 litres
Option 3: 5 litres
Option 4: 3 litres
Question : A container contains a 20 L mixture in which there is 10% sulphuric acid. Find the quantity of sulphuric acid to be added to it to make the solution contain 25% sulphuric acid.
Option 1: 2 L
Option 2: 3 L
Option 3: 4 L
Option 4: 5 L
Question : A 40 litres mixture contains 25% alcohol and 75% water. If 10 litres of water are added to the mixture, the percentage of alcohol in the new mixture is:
Option 1: 27%
Option 2: 18%
Option 3: 20%
Option 4: 25%
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