Question: A container contains 30 litres of milk. How many litres of water should be added to make the ratio of milk to water 5:2?
Solution: The container currently contains 30 litres of milk. Let’s assume we add x litres of water. According to the given ratio, the quantity of milk and water should be in the ratio of 5:2. So, we have the equation:
Cross-multiplying and solving for x, we get x = 12 litres.
Therefore, the answer is (b) 12 litres.
Question: A solution contains milk and water in the ratio of 3:2. How much water should be added to 20 litres of the solution to make the ratio 2:3?
Solution: The current ratio of milk to water is 3:2 in the given solution. We want to add x litres of water to make the new ratio 2:3. We can set up the equation:
Cross-multiplying and solving for x, we get x = 12 litres.
Therefore, the answer is (b) 12 litres.
Question: A mixture contains alcohol and water in the ratio of 5:2. How much water should be added to 60 litres of the mixture to make the ratio 2:3?
Solution: The current ratio of alcohol to water is 5:2 in the given mixture. We want to add x litres of water to make the new ratio 2:3. We can set up the equation:
Cross-multiplying and solving for x, we get x = 36 litres.
Therefore, the answer is (d) 36 litres.
Question: A container contains a mixture of milk and water in the ratio 4:1. If 10 litres of the mixture is taken out and replaced with water, the ratio becomes 3:1. What was the initial quantity of the mixture?
Solution: Let the initial quantity of the mixture be x litres. After taking out 10 litres and replacing it with water, the quantity of milk remains (4/5) * (x – 10) litres. The equation can be set up as follows:
(4/5) * (x – 10) / (x – 10 + 10) = 3/4
Solving for x, we get x = 40 litres.
Therefore, the answer is (d) 40 litres.
Question: A vessel contains 80 litres of a solution of milk and water in the ratio 5:3. How much of the mixture should be drawn off and replaced with water to make the ratio 3:5?
Solution: Let’s assume x litres of the mixture is drawn off and replaced with water. The quantity of milk remaining will be (5/8) * (80 – x) litres. The equation can be set up as follows:
(5/8) * (80 – x) / (80 – x + x) = 3/5
Solving for x, we get x = 30 litres.
Therefore, the answer is (c) 30 litres.
Question: A vessel contains a mixture of wine and water in the ratio 5:2. How much of the mixture should be drawn off and replaced with wine to make the ratio 7:3?
Solution: Let’s assume x litres of the mixture is drawn off and replaced with wine. The quantity of wine remaining will be (5/7) * (100 – x) litres. The equation can be set up as follows:
(5/7) * (100 – x) / (100 – x + x) = 7/10
Therefore, the answer is (a) 1/3.
Question: A vessel contains 60 litres of a mixture of milk and water in the ratio 2:3. How much of the mixture should be drawn off and replaced with milk to make the ratio 4:5?
Solution: Let’s assume x litres of the mixture is drawn off and replaced with milk. The quantity of milk remaining will be (2/5) * (60 – x) litres. The equation can be set up as follows:
(2/5) * (60 – x) / (60 – x + x) = 4/5
Solving for x, we get x = 20 litres.
Therefore, the answer is (d) 20 litres.
Question: A mixture of alcohol and water contains alcohol and water in the ratio 3:7. If 10 litres of the mixture is replaced with alcohol, the ratio becomes 4:6. What was the initial quantity of the mixture?
Solution: Let the initial quantity of the mixture be x litres. After replacing 10 litres with alcohol, the quantity of alcohol becomes (3/10) * (x – 10) litres. The equation can be set up as follows:
(3/10) * (x – 10) / (x – 10 + 10) = 4/6
Solving for x, we get x = 60 litres.
Therefore, the answer is (b) 60 litres.
Question: A container contains 100 litres of a mixture of milk and water in the ratio 3:2. How much of the mixture should be taken out and replaced with milk to make the ratio 5:4?
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (3/5) * (100 – x) litres. The equation can be set up as follows:
(3/5) * (100 – x) / (100 – x + x) = 5/9
Solving for x, we get x = 40 litres.
Therefore, the answer is (d) 40 litres.
Question: A vessel contains a mixture of wine and water in the ratio 4:5. If 40 litres of the mixture is drawn off and 10 litres of water is added, the ratio becomes 2:3. What was the initial quantity of the mixture?
Solution: Let the initial quantity of the mixture be x litres. After drawing off 40 litres and adding 10 litres of water, the quantity of wine becomes (4/9) * (x – 40 + 10) litres. The equation can be set up as follows:
(4/9) * (x – 30) / (x – 30 + 40) = 2/3
Solving for x, we get x = 120 litres.
Therefore, the answer is (d) 120 litres.
Question: A mixture contains alcohol and water in the ratio 3:7. How much of the mixture should be drawn off and replaced with water to make the ratio 2:5?
Solution: Let’s assume x litres of the mixture is drawn off and replaced with water. The quantity of alcohol remaining will be (3/10) * (100 – x) litres. The equation can be set up as follows:
(3/10) * (100 – x) / (100 – x + x) = 2/7
Therefore, the answer is (b) 3/4.
Question: A vessel contains a mixture of alcohol and water in the ratio 2:5. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 3:4?
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. The quantity of alcohol remaining will be (2/7) * (100 – x) litres. The equation can be set up as follows:
(2/7) * (100 – x) / (100 – x + x) = 3/4
Therefore, the answer is (c) 4/7.
Question: A container contains a mixture of milk and water in the ratio 2:3. How much of the mixture should be drawn off and replaced with milk to make the ratio 4:5?
Solution: Let’s assume x litres of the mixture is drawn off and replaced with milk. The quantity of milk remaining will be (2/5) * (100 – x) litres. The equation can be set up as follows:
(2/5) * (100 – x) / (100 – x + x) = 4/9
Therefore, the answer is (a) 3/5.
Question: A mixture contains alcohol and water in the ratio 5:3. How much of the mixture should be drawn off and replaced with water to make the ratio 3:4?
Solution: Let’s assume x litres of the mixture is drawn off and replaced with water. The quantity of alcohol remaining will be (5/8) * (100 – x) litres. The equation can be set up as follows: