Question : A container contains 25 litres of milk. From this container, 5 litres of milk is taken out and replaced by water. This process is further repeated two times. How much milk is there in the container now?
Option 1: 11.5 litres
Option 2: 14.8 litres
Option 3: 13.5 litres
Option 4: 12.8 litres
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Correct Answer: 12.8 litres
Solution : Left quantity = Initial quantity(1 – [Fraction removed])N (Where N = Number of times the process is carried out) Fraction of milk removed = $\frac{5}{25}$ = $\frac{1}{5}$ Now, the quantity of milk left in the container $= 25(1 - \frac{1}{5})^3$ $= 25 × (\frac{4}{5})^3$ $= 25 × \frac{64}{125}$ $= 12.8$ litres ∴ There are 12.8 litres of milk left in the container. Hence, the correct answer is 12.8 litres.
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Question : 40 litres of milk are kept in a container. 4 litres of milk were removed from this container and replaced with water. This procedure was performed two more times. How much milk does the container now hold?
Option 1: 30 litres
Option 2: 34.23 litres
Option 3: 29.16 litres
Option 4: 32 litres
Question : The ratio of milk to water in a 100-litres mixture is 2 : 3. 10 litres of this mixture is withdrawn and replaced with milk. This process is repeated 2 more times. What is the percentage of milk in the final mixture?
Option 1: 56.26%
Option 2: 54.27%
Option 3: 58.21%
Option 4: 51.24%
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 : In a mixture of 25 litres, the ratio of milk to water is 4 : 1. Another 3 litres of water is added to the mixture. The ratio of milk to water in the new mixture is:
Option 1: 5 : 1
Option 2: 5 : 2
Option 3: 5 : 3
Option 4: 5 : 4
Question : A can of water and milk mixture contains 60% milk. A part of this mixture is replaced by another mixture containing 50% milk and the percentage of milk was found to be 52%. The quantity of mixture replaced is:
Option 1: $\frac{1}{5}$
Option 2: $\frac{3}{5}$
Option 3: $\frac{4}{5}$
Option 4: $\frac{2}{5}$
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