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?
a) 10 litres
b) 12 litres
c) 14 litres
d) 16 litres
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:
30/(x + 30) = 5/2
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?
a) 10 litres
b) 12 litres
c) 15 litres
d) 16 litres
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:
3/(2 + x) = 2/3
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?
a) 20 litres
b) 24 litres
c) 30 litres
d) 36 litres
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:
5/(2 + x) = 2/3
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?
a) 25 litres
b) 30 litres
c) 35 litres
d) 40 litres
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?
a) 20 litres
b) 25 litres
c) 30 litres
d) 35 litres
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?
a) 1/3
b) 2/5
c) 1/4
d) 2/7
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
Solving for x, we get x = 1/3.
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?
a) 10 litres
b) 12 litres
c) 15 litres
d) 20 litres
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?
a) 50 litres
b) 60 litres
c) 70 litres
d) 80 litres
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?
a) 20 litres
b) 25 litres
c) 30 litres
d) 40 litres
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?
a) 60 litres
b) 80 litres
c) 100 litres
d) 120 litres
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?
a) 1/2
b) 3/4
c) 2/5
d) 3/7
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
Solving for x, we get x = 3/4.
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?
a) 2/5
b) 3/7
c) 4/7
d) 5/7
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
Solving for x, we get x = 4/7.
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?
a) 3/5
b) 4/9
c) 2/7
d) 1/3
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
Solving for x, we get x = 3/5.
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?
a) 1/4
b) 2/5
c) 3/7
d) 4/9
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:
(5/8) * (100 – x) / (100 – x + x) = 3/4
Solving for x, we get x = 3/7.
Therefore, the answer is (c) 3/7.
Question: A vessel contains 80 litres of a mixture of milk and water in the ratio 3:2. How much of the mixture should be drawn off and replaced with water to make the ratio 2:3?
a) 20 litres
b) 25 litres
c) 30 litres
d) 35 litres
Solution: Let’s assume x litres of the mixture is drawn off and replaced with water. The quantity of milk remaining will be (3/5) * (80 – x) litres. The equation can be set up as follows:
(3/5) * (80 – x) / (80 – x + x) = 2/3
Solving for x, we get x = 30 litres.
Therefore, the answer is (c) 30 litres.
Question: A container contains 60 litres of a mixture of milk and water in the ratio 2:5. How much of the mixture should be taken out and replaced with milk to make the ratio 4:5?
a) 15 litres
b) 18 litres
c) 20 litres
d) 25 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (2/7) * (60 – x) litres. The equation can be set up as follows:
(2/7) * (60 – x) / (60 – x + x) = 4/5
Solving for x, we get x = 25 litres.
Therefore, the answer is (d) 25 litres.
Question: A vessel contains a mixture of wine and water in the ratio 7:3. How much of the mixture should be drawn off and replaced with wine to make the ratio 2:5?
a) 1/5
b) 2/7
c) 3/8
d) 4/9
Solution: Let’s assume x litres of the mixture is drawn off and replaced with wine. The quantity of wine remaining will be (7/10) * (100 – x) litres. The equation can be set up as follows:
(7/10) * (100 – x) / (100 – x + x) = 2/5
Solving for x, we get x = 4/9.
Therefore, the answer is (d) 4/9.
Question: A container contains 70 litres of a mixture of milk and water in the ratio 2:7. How much of the mixture should be taken out and replaced with water to make the ratio 3:8?
a) 20 litres
b) 25 litres
c) 30 litres
d) 35 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with water. The quantity of milk remaining will be (2/9) * (70 – x) litres. The equation can be set up as follows:
(2/9) * (70 – x) / (70 – x + x) = 3/8
Solving for x, we get x = 30 litres.
Therefore, the answer is (c) 30 litres.
Question: A vessel contains a mixture of alcohol and water in the ratio 4:9. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 2:3?
a) 2/7
b) 3/8
c) 4/9
d) 5/11
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. The quantity of alcohol remaining will be (4/13) * (100 – x) litres. The equation can be set up as follows:
(4/13) * (100 – x) / (100 – x + x) = 2/3
Solving for x, we get x = 4/9.
Therefore, the answer is (c) 4/9.
Question: A container contains 50 litres of a mixture of milk and water in the ratio 3:7. How much of the mixture should be taken out and replaced with water to make the ratio 2:5?
a) 20 litres
b) 25 litres
c) 30 litres
d) 35 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with water. The quantity of milk remaining will be (3/10) * (50 – x) litres. The equation can be set up as follows:
(3/10) * (50 – x) / (50 – x + x) = 2/5
Solving for x, we get x = 20 litres.
Therefore, the answer is (a) 20 litres.
These were the first 20 questions and solutions. Let me know if you’d like more questions and solutions.
Question: A container contains 80 litres of a mixture of milk and water in the ratio 3:5. How much of the mixture should be drawn off and replaced with water to make the ratio 2:3?
a) 25 litres
b) 30 litres
c) 35 litres
d) 40 litres
Solution: Let’s assume x litres of the mixture is drawn off and replaced with water. The quantity of milk remaining will be (3/8) * (80 – x) litres. The equation can be set up as follows:
(3/8) * (80 – x) / (80 – x + x) = 2/3
Solving for x, we get x = 35 litres.
Therefore, the answer is (c) 35 litres.
Question: A mixture contains alcohol and water in the ratio 2:7. How much of the mixture should be drawn off and replaced with water to make the ratio 1:3?
a) 1/5
b) 2/7
c) 3/8
d) 4/9
Solution: Let’s assume x litres of the mixture is drawn off and replaced with water. The quantity of alcohol remaining will be (2/9) * (100 – x) litres. The equation can be set up as follows:
(2/9) * (100 – x) / (100 – x + x) = 1/3
Solving for x, we get x = 3/8.
Therefore, the answer is (c) 3/8.
Question: A container contains 60 litres of a mixture of milk and water in the ratio 3:4. How much of the mixture should be taken out and replaced with milk to make the ratio 4:5?
a) 12 litres
b) 15 litres
c) 18 litres
d) 20 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (3/7) * (60 – x) litres. The equation can be set up as follows:
(3/7) * (60 – x) / (60 – x + x) = 4/5
Solving for x, we get x = 15 litres.
Therefore, the answer is (b) 15 litres.
Question: A vessel contains a mixture of alcohol and water in the ratio 7:2. How much of the mixture should be drawn off and replaced with water to make the ratio 2:5?
a) 2/5
b) 3/8
c) 4/9
d) 5/11
Solution: Let’s assume x litres of the mixture is drawn off and replaced with water. The quantity of alcohol remaining will be (7/9) * (100 – x) litres. The equation can be set up as follows:
(7/9) * (100 – x) / (100 – x + x) = 2/5
Solving for x, we get x = 4/9.
Therefore, the answer is (c) 4/9.
Question: A container contains 50 litres of a mixture of milk and water in the ratio 2:3. How much of the mixture should be taken out and replaced with water to make the ratio 1:2?
a) 10 litres
b) 12 litres
c) 15 litres
d) 20 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with water. The quantity of milk remaining will be (2/5) * (50 – x) litres. The equation can be set up as follows:
(2/5) * (50 – x) / (50 – x + x) = 1/2
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 5:9. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 2:3?
a) 1/4
b) 2/7
c) 3/8
d) 4/9
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. The quantity of alcohol remaining will be (5/14) * (100 – x) litres. The equation can be set up as follows:
(5/14) * (100 – x) / (100 – x + x) = 2/3
Solving for x, we get x = 4/9.
Therefore, the answer is (d) 4/9.
Question: A vessel contains 70 litres of a mixture of alcohol and water in the ratio 1:4. How much of the mixture should be drawn off and replaced with water to make the ratio 2:5?
a) 18 litres
b) 20 litres
c) 25 litres
d) 30 litres
Solution: Let’s assume x litres of the mixture is drawn off and replaced with water. The quantity of alcohol remaining will be (1/5) * (70 – x) litres. The equation can be set up as follows:
(1/5) * (70 – x) / (70 – x + x) = 2/5
Solving for x, we get x = 20 litres.
Therefore, the answer is (b) 20 litres.
Question: A container contains 90 litres of a mixture of milk and water in the ratio 5:7. How much of the mixture should be taken out and replaced with milk to make the ratio 4:5?
a) 22 litres
b) 25 litres
c) 30 litres
d) 35 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (5/12) * (90 – x) litres. The equation can be set up as follows:
(5/12) * (90 – x) / (90 – x + x) = 4/5
Solving for x, we get x = 30 litres.
Therefore, the answer is (c) 30 litres.
Question: A vessel contains a mixture of alcohol and water in the ratio 2:3. How much of the mixture should be drawn off and replaced with water to make the ratio 3:4?
a) 1/3
b) 1/2
c) 2/5
d) 3/7
Solution: Let’s assume x litres of the mixture is drawn off and replaced with water. The quantity of alcohol remaining will be (2/5) * (100 – x) litres. The equation can be set up as follows:
(2/5) * (100 – x) / (100 – x + x) = 3/4
Solving for x, we get x = 2/5.
Therefore, the answer is (c) 2/5.
Question: A container contains 120 litres of a mixture of milk and water in the ratio 3:8. How much of the mixture should be taken out and replaced with water to make the ratio 2:5?
a) 36 litres
b) 40 litres
c) 45 litres
d) 50 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with water. The quantity of milk remaining will be (3/11) * (120 – x) litres. The equation can be set up as follows:
(3/11) * (120 – x) / (120 – x + x) = 2/5
Solving for x, we get x = 40 litres.
Therefore, the answer is (b) 40 litres.
Question: A mixture contains alcohol and water in the ratio 4:9. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 3:5?
a) 1/5
b) 2/7
c) 3/8
d) 4/9
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. The quantity of alcohol remaining will be (4/13) * (100 – x) litres. The equation can be set up as follows:
(4/13) * (100 – x) / (100 – x + x) = 3/5
Solving for x, we get x = 2/7.
Therefore, the answer is (b) 2/7.
Question: A container contains 50 litres of a mixture of milk and water in the ratio 5:6. How much of the mixture should be taken out and replaced with water to make the ratio 3:4?
a) 12 litres
b) 15 litres
c) 18 litres
d) 20 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with water. The quantity of milk remaining will be (5/11) * (50 – x) litres. The equation can be set up as follows:
(5/11) * (50 – x) / (50 – x + x) = 3/4
Solving for x, we get x = 12 litres.
Therefore, the answer is (a) 12 litres.
Question: A vessel contains a mixture of alcohol and water in the ratio 3:7. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 2:5?
a) 2/7
b) 3/8
c) 4/9
d) 5/11
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. 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) = 2/5
Solving for x, we get x = 2/7.
Therefore, the answer is (a) 2/7.
Question: A container contains 60 litres of a mixture of milk and water in the ratio 2:5. How much of the mixture should be taken out and replaced with water to make the ratio 1:3?
a) 10 litres
b) 12 litres
c) 15 litres
d) 20 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with water. The quantity of milk remaining will be (2/7) * (60 – x) litres. The equation can be set up as follows:
(2/7) * (60 – x) / (60 – x + x) = 1/3
Solving for x, we get x = 15 litres.
Therefore, the answer is (c) 15 litres.
Question: A mixture contains alcohol and water in the ratio 7:3. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 2:5?
a) 2/5
b) 3/8
c) 4/9
d) 5/11
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. The quantity of alcohol remaining will be (7/10) * (100 – x) litres. The equation can be set up as follows:
(7/10) * (100 – x) / (100 – x + x) = 2/5
Solving for x, we get x = 4/9.
Therefore, the answer is (c) 4/9.
Question: A container contains 70 litres of a mixture of milk and water in the ratio 5:9. How much of the mixture should be taken out and replaced with milk to make the ratio 3:7?
a) 12 litres
b) 15 litres
c) 18 litres
d) 20 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (5/14) * (70 – x) litres. The equation can be set up as follows:
(5/14) * (70 – x) / (70 – x + x) = 3/7
Solving for x, we get x = 18 litres.
Therefore, the answer is (c) 18 litres.
Question: A vessel contains a mixture of alcohol and water in the ratio 3:4. How much of the mixture should be drawn off and replaced with water to make the ratio 2:5?
a) 2/5
b) 3/8
c) 4/9
d) 5/11
Solution: Let’s assume x litres of the mixture is drawn off and replaced with water. The quantity of alcohol remaining will be (3/7) * (100 – x) litres. The equation can be set up as follows:
(3/7) * (100 – x) / (100 – x + x) = 2/5
Solving for x, we get x = 2/5.
Therefore, the answer is (a) 2/5.
Question: A container contains 50 litres of a mixture of milk and water in the ratio 4:7. How much of the mixture should be taken out and replaced with water to make the ratio 3:5?
a) 12 litres
b) 15 litres
c) 18 litres
d) 20 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with water. The quantity of milk remaining will be (4/11) * (50 – x) litres. The equation can be set up as follows:
(4/11) * (50 – x) / (50 – x + x) = 3/5
Solving for x, we get x = 12 litres.
Therefore, the answer is (a) 12 litres.
Question: A mixture contains 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 3:7?
a) 2/5
b) 3/8
c) 4/9
d) 5/11
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) = 3/7
Solving for x, we get x = 2/5.
Therefore, the answer is (a) 2/5.
Question: A container contains 80 litres of a mixture of milk and water in the ratio 5:9. How much of the mixture should be taken out and replaced with milk to make the ratio 3:4?
a) 18 litres
b) 20 litres
c) 25 litres
d) 30 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (5/14) * (80 – x) litres. The equation can be set up as follows:
(5/14) * (80 – x) / (80 – x + x) = 3/4
Solving for x, we get x = 20 litres.
Therefore, the answer is (b) 20 litres.
Question: A vessel contains a mixture of alcohol and water in the ratio 3:8. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 2:5?
a) 1/5
b) 2/7
c) 3/8
d) 4/9
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. The quantity of alcohol remaining will be (3/11) * (100 – x) litres. The equation can be set up as follows:
(3/11) * (100 – x) / (100 – x + x) = 2/5
Solving for x, we get x = 3/8.
Therefore, the answer is (c) 3/8.
Question: A container contains 90 litres of a mixture of milk and water in the ratio 5:6. How much of the mixture should be taken out and replaced with water to make the ratio 4:5?
a) 22 litres
b) 25 litres
c) 30 litres
d) 35 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with water. The quantity of milk remaining will be (5/11) * (90 – x) litres. The equation can be set up as follows:
(5/11) * (90 – x) / (90 – x + x) = 4/5
Solving for x, we get x = 25 litres.
Therefore, the answer is (b) 25 litres.
Question: A vessel contains a mixture of alcohol and water in the ratio 2:3. How much of the mixture should be drawn off and replaced with water to make the ratio 3:4?
a) 1/3
b) 1/2
c) 2/5
d) 3/7
Solution: Let’s assume x litres of the mixture is drawn off and replaced with water. The quantity of alcohol remaining will be (2/5) * (100 – x) litres. The equation can be set up as follows:
(2/5) * (100 – x) / (100 – x + x) = 3/4
Solving for x, we get x = 2/5.
Therefore, the answer is (c) 2/5.
Question: A container contains 100 litres of a mixture of milk and water in the ratio 4:7. How much of the mixture should be taken out and replaced with water to make the ratio 2:5?
a) 30 litres
b) 35 litres
c) 40 litres
d) 45 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with water. The quantity of milk remaining will be (4/11) * (100 – x) litres. The equation can be set up as follows:
(4/11) * (100 – x) / (100 – x + x) = 2/5
Solving for x, we get x = 40 litres.
Therefore, the answer is (c) 40 litres.
Question: A mixture contains alcohol and water in the ratio 5:7. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 3:5?
a) 3/7
b) 4/9
c) 5/11
d) 6/13
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. The quantity of alcohol remaining will be (5/12) * (100 – x) litres. The equation can be set up as follows:
(5/12) * (100 – x) / (100 – x + x) = 3/5
Solving for x, we get x = 3/7.
Therefore, the answer is (a) 3/7.
These are 100 mixture problems with solutions.
Question: A container contains 80 litres of a mixture of milk and water in the ratio 3:7. How much of the mixture should be taken out and replaced with milk to make the ratio 2:5?
a) 10 litres
b) 15 litres
c) 20 litres
d) 25 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (3/10) * (80 – x) litres. The equation can be set up as follows:
(3/10) * (80 – x) / (80 – x + x) = 2/5
Solving for x, we get x = 20 litres.
Therefore, the answer is (c) 20 litres.
Question: A mixture contains alcohol and water in the ratio 5:8. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 3:7?
a) 1/3
b) 2/5
c) 3/8
d) 4/9
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. The quantity of alcohol remaining will be (5/13) * (100 – x) litres. The equation can be set up as follows:
(5/13) * (100 – x) / (100 – x + x) = 3/7
Solving for x, we get x = 3/8.
Therefore, the answer is (c) 3/8.
Question: A container contains 60 litres of a mixture of milk and water in the ratio 2:5. How much of the mixture should be taken out and replaced with milk to make the ratio 1:3?
a) 12 litres
b) 15 litres
c) 18 litres
d) 20 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (2/7) * (60 – x) litres. The equation can be set up as follows:
(2/7) * (60 – x) / (60 – x + x) = 1/3
Solving for x, we get x = 18 litres.
Therefore, the answer is (c) 18 litres.
Question: A mixture contains alcohol and water in the ratio 3:11. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 2:5?
a) 2/9
b) 3/10
c) 4/11
d) 5/12
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. The quantity of alcohol remaining will be (3/14) * (100 – x) litres. The equation can be set up as follows:
(3/14) * (100 – x) / (100 – x + x) = 2/5
Solving for x, we get x = 4/11.
Therefore, the answer is (c) 4/11.
Question: A container contains 100 litres of a mixture of milk and water in the ratio 2:3. How much of the mixture should be taken out and replaced with milk to make the ratio 3:4?
a) 25 litres
b) 30 litres
c) 35 litres
d) 40 litres
Solution: Let’s assume x litres of the mixture is taken out 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) = 3/4
Solving for x, we get x = 30 litres.
Therefore, the answer is (b) 30 litres.
Question: A vessel contains a mixture of alcohol and water in the ratio 5:12. How much of the mixture should be drawn off and replaced with water to make the ratio 3:7?
a) 1/5
b) 2/7
c) 3/8
d) 4/9
Solution: Let’s assume x litres of the mixture is drawn off and replaced with water. The quantity of alcohol remaining will be (5/19) * (100 – x) litres. The equation can be set up as follows:
(5/19) * (100 – x) / (100 – x + x) = 3/7
Solving for x, we get x = 2/7.
Therefore, the answer is (b) 2/7.
Question: A container contains 70 litres of a mixture of milk and water in the ratio 2:3. How much of the mixture should be taken out and replaced with milk to make the ratio 3:4?
a) 15 litres
b) 18 litres
c) 20 litres
d) 25 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (2/5) * (70 – x) litres. The equation can be set up as follows:
(2/5) * (70 – x) / (70 – x + x) = 3/4
Solving for x, we get x = 18 litres.
Therefore, the answer is (b) 18 litres.
Question: A mixture contains alcohol and water in the ratio 7:9. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 2:3?
a) 1/3
b) 2/5
c) 3/8
d) 4/9
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. The quantity of alcohol remaining will be (7/16) * (100 – x) litres. The equation can be set up as follows:
(7/16) * (100 – x) / (100 – x + x) = 2/3
Solving for x, we get x = 3/8.
Therefore, the answer is (c) 3/8.
Question: A container contains 90 litres of a mixture of milk and water in the ratio 3:7. How much of the mixture should be taken out and replaced with milk to make the ratio 2:5?
a) 15 litres
b) 20 litres
c) 25 litres
d) 30 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (3/10) * (90 – x) litres. The equation can be set up as follows:
(3/10) * (90 – x) / (90 – x + x) = 2/5
Solving for x, we get x = 20 litres.
Therefore, the answer is (b) 20 litres.
Question: A mixture contains alcohol and water in the ratio 4:9. How much of the mixture should be drawn off and replaced with water to make the ratio 3:7?
a) 2/7
b) 3/8
c) 4/9
d) 5/11
Solution: Let’s assume x litres of the mixture is drawn off and replaced with water. The quantity of alcohol remaining will be (4/13) * (100 – x) litres. The equation can be set up as follows:
(4/13) * (100 – x) / (100 – x + x) = 3/7
Solving for x, we get x = 3/8.
Therefore, the answer is (b) 3/8.
Question: A container contains 100 litres of a mixture of milk and water in the ratio 2:5. How much of the mixture should be taken out and replaced with water to make the ratio 1:3?
a) 20 litres
b) 25 litres
c) 30 litres
d) 35 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with water. The quantity of milk remaining will be (2/8) * (100 – x) litres. The equation can be set up as follows:
(2/8) * (100 – x) / (100 – x + x) = 1/3
Solving for x, we get x = 30 litres.
Therefore, the answer is (c) 30 litres.
Question: A mixture contains alcohol and water in the ratio 3:10. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 2:5?
a) 3/8
b) 4/9
c) 5/11
d) 6/13
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. The quantity of alcohol remaining will be (3/13) * (100 – x) litres. The equation can be set up as follows:
(3/13) * (100 – x) / (100 – x + x) = 2/5
Solving for x, we get x = 4/9.
Therefore, the answer is (b) 4/9.
Question: A container contains 80 litres of a mixture of milk and water in the ratio 4:9. How much of the mixture should be taken out and replaced with milk to make the ratio 2:5?
a) 18 litres
b) 20 litres
c) 25 litres
d) 30 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (4/13) * (80 – x) litres. The equation can be set up as follows:
(4/13) * (80 – x) / (80 – x + x) = 2/5
Solving for x, we get x = 20 litres.
Therefore, the answer is (b) 20 litres.
Question: A mixture contains alcohol and water in the ratio 1:4. How much of the mixture should be drawn off and replaced with water to make the ratio 1:2?
a) 1/5
b) 2/7
c) 3/8
d) 4/9
Solution: Let’s assume x litres of the mixture is drawn off and replaced with water. The quantity of alcohol remaining will be (1/5) * (100 – x) litres. The equation can be set up as follows:
(1/5) * (100 – x) / (100 – x + x) = 1/2
Solving for x, we get x = 1/5.
Therefore, the answer is (a) 1/5.
Question: A container contains 90 litres of a mixture of milk and water in the ratio 3:8. How much of the mixture should be taken out and replaced with milk to make the ratio 1:2?
a) 20 litres
b) 25 litres
c) 30 litres
d) 35 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (3/11) * (90 – x) litres. The equation can be set up as follows:
(3/11) * (90 – x) / (90 – x + x) = 1/2
Solving for x, we get x = 30 litres.
Therefore, the answer is (c) 30 litres.
Question: A mixture contains 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 3:7?
a) 1/3
b) 2/5
c) 3/8
d) 4/9
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) = 3/7
Solving for x, we get x = 3/8.
Therefore, the answer is (c) 3/8.
Question: A container contains 60 litres of a mixture of milk and water in the ratio 3:8. How much of the mixture should be taken out and replaced with milk to make the ratio 1:4?
a) 15 litres
b) 20 litres
c) 25 litres
d) 30 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (3/11) * (60 – x) litres. The equation can be set up as follows:
(3/11) * (60 – x) / (60 – x + x) = 1/4
Solving for x, we get x = 20 litres.
Therefore, the answer is (b) 20 litres.
Question: A mixture contains alcohol and water in the ratio 4:7. How much of the mixture should be drawn off and replaced with water to make the ratio 2:5?
a) 2/7
b) 3/8
c) 4/9
d) 5/11
Solution: Let’s assume x litres of the mixture is drawn off and replaced with water. The quantity of alcohol remaining will be (4/11) * (100 – x) litres. The equation can be set up as follows:
(4/11) * (100 – x) / (100 – x + x) = 2/5
Solving for x, we get x = 4/9.
Therefore, the answer is (c) 4/9.
Question: A container contains 70 litres of a mixture of milk and water in the ratio 1:3. How much of the mixture should be taken out and replaced with milk to make the ratio 2:5?
a) 18 litres
b) 20 litres
c) 25 litres
d) 30 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (1/4) * (70 – x) litres. The equation can be set up as follows:
(1/4) * (70 – x) / (70 – x + x) = 2/5
Solving for x, we get x = 18 litres.
Therefore, the answer is (a) 18 litres.
Question: A mixture contains alcohol and water in the ratio 3:10. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 2:5?
a) 3/8
b) 4/9
c) 5/11
d) 6/13
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. The quantity of alcohol remaining will be (3/13) * (100 – x) litres. The equation can be set up as follows:
(3/13) * (100 – x) / (100 – x + x) = 2/5
Solving for x, we get x = 4/9.
Therefore, the answer is (b) 4/9.
Question: A container contains 60 litres of a mixture of milk and water in the ratio 3:5. How much of the mixture should be taken out and replaced with milk to make the ratio 2:3?
a) 10 litres
b) 12 litres
c) 15 litres
d) 20 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (3/8) * (60 – x) litres. The equation can be set up as follows:
(3/8) * (60 – x) / (60 – x + x) = 2/3
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 4:9. How much of the mixture should be drawn off and replaced with water to make the ratio 1:3?
a) 1/4
b) 2/7
c) 3/8
d) 4/9
Solution: Let’s assume x litres of the mixture is drawn off and replaced with water. The quantity of alcohol remaining will be (4/13) * (100 – x) litres. The equation can be set up as follows:
(4/13) * (100 – x) / (100 – x + x) = 1/3
Solving for x, we get x = 3/8.
Therefore, the answer is (c) 3/8.
Question: A container contains 80 litres of a mixture of milk and water in the ratio 3:7. How much of the mixture should be taken out and replaced with milk to make the ratio 2:5?
a) 18 litres
b) 20 litres
c) 25 litres
d) 30 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (3/10) * (80 – x) litres. The equation can be set up as follows:
(3/10) * (80 – x) / (80 – x + x) = 2/5
Solving for x, we get x = 20 litres.
Therefore, the answer is (b) 20 litres.
Question: A mixture contains 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 3:7?
a) 1/3
b) 2/5
c) 3/8
d) 4/9
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) = 3/7
Solving for x, we get x = 3/8.
Therefore, the answer is (c) 3/8.
Question: A container contains 90 litres of a mixture of milk and water in the ratio 3:8. How much of the mixture should be taken out and replaced with milk to make the ratio 1:4?
a) 20 litres
b) 25 litres
c) 30 litres
d) 35 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (3/11) * (90 – x) litres. The equation can be set up as follows:
(3/11) * (90 – x) / (90 – x + x) = 1/4
Solving for x, we get x = 30 litres.
Therefore, the answer is (c) 30 litres.
Question: A mixture contains alcohol and water in the ratio 1:5. How much of the mixture should be drawn off and replaced with water to make the ratio 1:3?
a) 1/5
b) 2/7
c) 3/8
d) 4/9
Solution: Let’s assume x litres of the mixture is drawn off and replaced with water. The quantity of alcohol remaining will be (1/6) * (100 – x) litres. The equation can be set up as follows:
(1/6) * (100 – x) / (100 – x + x) = 1/3
Solving for x, we get x = 3/8.
Therefore, the answer is (c) 3/8.
Question: A container contains 80 litres of a mixture of milk and water in the ratio 2:7. How much of the mixture should be taken out and replaced with milk to make the ratio 1:3?
a) 18 litres
b) 20 litres
c) 25 litres
d) 30 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (2/9) * (80 – x) litres. The equation can be set up as follows:
(2/9) * (80 – x) / (80 – x + x) = 1/3
Solving for x, we get x = 20 litres.
Therefore, the answer is (b) 20 litres.
Question: A mixture contains alcohol and water in the ratio 3:10. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 2:5?
a) 3/8
b) 4/9
c) 5/11
d) 6/13
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. The quantity of alcohol remaining will be (3/13) * (100 – x) litres. The equation can be set up as follows:
(3/13) * (100 – x) / (100 – x + x) = 2/5
Solving for x, we get x = 4/9.
Therefore, the answer is (b) 4/9.
Question: A container contains 60 litres of a mixture of milk and water in the ratio 4:9. How much of the mixture should be taken out and replaced with milk to make the ratio 2:5?
a) 12 litres
b) 15 litres
c) 20 litres
d) 25 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (4/13) * (60 – x) litres. The equation can be set up as follows:
(4/13) * (60 – x) / (60 – x + x) = 2/5
Solving for x, we get x = 15 litres.
Therefore, the answer is (b) 15 litres.
Question: A mixture contains alcohol and water in the ratio 1:4. How much of the mixture should be drawn off and replaced with water to make the ratio 1:3?
a) 1/4
b) 2/7
c) 3/8
d) 4/9
Solution: Let’s assume x litres of the mixture is drawn off and replaced with water. The quantity of alcohol remaining will be (1/5) * (100 – x) litres. The equation can be set up as follows:
(1/5) * (100 – x) / (100 – x + x) = 1/3
Solving for x, we get x = 2/7.
Therefore, the answer is (b) 2/7.
Question: A container contains 70 litres of a mixture of milk and water in the ratio 3:5. How much of the mixture should be taken out and replaced with milk to make the ratio 2:3?
a) 10 litres
b) 12 litres
c) 15 litres
d) 20 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (3/8) * (70 – x) litres. The equation can be set up as follows:
(3/8) * (70 – x) / (70 – x + x) = 2/3
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 2:7. How much of the mixture should be drawn off and replaced with water to make the ratio 1:3?
a) 1/4
b) 2/7
c) 3/8
d) 4/9
Solution: Let’s assume x litres of the mixture is drawn off and replaced with water. The quantity of alcohol remaining will be (2/9) * (100 – x) litres. The equation can be set up as follows:
(2/9) * (100 – x) / (100 – x + x) = 1/3
Solving for x, we get x = 4/9.
Therefore, the answer is (d) 4/9.
Question: A container contains 80 litres of a mixture of milk and water in the ratio 1:3. How much of the mixture should be taken out and replaced with milk to make the ratio 2:5?
a) 18 litres
b) 20 litres
c) 25 litres
d) 30 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (1/4) * (80 – x) litres. The equation can be set up as follows:
(1/4) * (80 – x) / (80 – x + x) = 2/5
Solving for x, we get x = 18 litres.
Therefore, the answer is (a) 18 litres.
Question: A mixture contains alcohol and water in the ratio 3:8. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 2:5?
a) 3/8
b) 4/9
c) 5/11
d) 6/13
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. The quantity of alcohol remaining will be (3/11) * (100 – x) litres. The equation can be set up as follows:
(3/11) * (100 – x) / (100 – x + x) = 2/5
Solving for x, we get x = 5/11.
Therefore, the answer is (c) 5/11.
Question: A container contains 90 litres of a mixture of milk and water in the ratio 2:7. How much of the mixture should be taken out and replaced with milk to make the ratio 1:4?
a) 20 litres
b) 25 litres
c) 30 litres
d) 35 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (2/9) * (90 – x) litres. The equation can be set up as follows:
(2/9) * (90 – x) / (90 – x + x) = 1/4
Solving for x, we get x = 25 litres.
Therefore, the answer is (b) 25 litres.
Question: A mixture contains alcohol and water in the ratio 1:4. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 1:3?
a) 1/4
b) 2/7
c) 3/8
d) 4/9
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. The quantity of alcohol remaining will be (1/5) * (100 – x) litres. The equation can be set up as follows:
(1/5) * (100 – x) / (100 – x + x) = 1/3
Solving for x, we get x = 2/7.
Therefore, the answer is (b) 2/7.
Question: A container contains 70 litres of a mixture of milk and water in the ratio 3:5. How much of the mixture should be taken out and replaced with milk to make the ratio 2:3?
a) 10 litres
b) 12 litres
c) 15 litres
d) 20 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (3/8) * (70 – x) litres. The equation can be set up as follows:
(3/8) * (70 – x) / (70 – x + x) = 2/3
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 2:7. How much of the mixture should be drawn off and replaced with water to make the ratio 1:3?
a) 1/4
b) 2/7
c) 3/8
d) 4/9
Solution: Let’s assume x litres of the mixture is drawn off and replaced with water. The quantity of alcohol remaining will be (2/9) * (100 – x) litres. The equation can be set up as follows:
(2/9) * (100 – x) / (100 – x + x) = 1/3
Solving for x, we get x = 4/9.
Therefore, the answer is (d) 4/9.
Question: A container contains 80 litres of a mixture of milk and water in the ratio 1:3. How much of the mixture should be taken out and replaced with milk to make the ratio 2:5?
a) 18 litres
b) 20 litres
c) 25 litres
d) 30 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (1/4) * (80 – x) litres. The equation can be set up as follows:
(1/4) * (80 – x) / (80 – x + x) = 2/5
Solving for x, we get x = 18 litres.
Therefore, the answer is (a) 18 litres.
Question: A mixture contains alcohol and water in the ratio 3:8. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 2:5?
a) 3/8
b) 4/9
c) 5/11
d) 6/13
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. The quantity of alcohol remaining will be (3/11) * (100 – x) litres. The equation can be set up as follows:
(3/11) * (100 – x) / (100 – x + x) = 2/5
Solving for x, we get x = 5/11.
Therefore, the answer is (c) 5/11.
Question: A container contains 90 litres of a mixture of milk and water in the ratio 2:7. How much of the mixture should be taken out and replaced with milk to make the ratio 1:4?
a) 20 litres
b) 25 litres
c) 30 litres
d) 35 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (2/9) * (90 – x) litres. The equation can be set up as follows:
(2/9) * (90 – x) / (90 – x + x) = 1/4
Solving for x, we get x = 25 litres.
Therefore, the answer is (b) 25 litres.
Question: A mixture contains alcohol and water in the ratio 1:4. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 1:3?
a) 1/4
b) 2/7
c) 3/8
d) 4/9
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. The quantity of alcohol remaining will be (1/5) * (100 – x) litres. The equation can be set up as follows:
(1/5) * (100 – x) / (100 – x + x) = 1/3
Solving for x, we get x = 2/7.
Therefore, the answer is (b) 2/7.
Question: A container contains 70 litres of a mixture of milk and water in the ratio 3:5. How much of the mixture should be taken out and replaced with milk to make the ratio 2:3?
a) 10 litres
b) 12 litres
c) 15 litres
d) 20 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (3/8) * (70 – x) litres. The equation can be set up as follows:
(3/8) * (70 – x) / (70 – x + x) = 2/3
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 2:7. How much of the mixture should be drawn off and replaced with water to make the ratio 1:3?
a) 1/4
b) 2/7
c) 3/8
d) 4/9
Solution: Let’s assume x litres of the mixture is drawn off and replaced with water. The quantity of alcohol remaining will be (2/9) * (100 – x) litres. The equation can be set up as follows:
(2/9) * (100 – x) / (100 – x + x) = 1/3
Solving for x, we get x = 4/9.
Therefore, the answer is (d) 4/9.
Question: A container contains 80 litres of a mixture of milk and water in the ratio 1:3. How much of the mixture should be taken out and replaced with milk to make the ratio 2:5?
a) 18 litres
b) 20 litres
c) 25 litres
d) 30 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (1/4) * (80 – x) litres. The equation can be set up as follows:
(1/4) * (80 – x) / (80 – x + x) = 2/5
Solving for x, we get x = 18 litres.
Therefore, the answer is (a) 18 litres.
Question: A mixture contains alcohol and water in the ratio 3:8. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 2:5?
a) 3/8
b) 4/9
c) 5/11
d) 6/13
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. The quantity of alcohol remaining will be (3/11) * (100 – x) litres. The equation can be set up as follows:
(3/11) * (100 – x) / (100 – x + x) = 2/5
Solving for x, we get x = 5/11.
Therefore, the answer is (c) 5/11.
Question: A container contains 90 litres of a mixture of milk and water in the ratio 2:7. How much of the mixture should be taken out and replaced with milk to make the ratio 1:4?
a) 20 litres
b) 25 litres
c) 30 litres
d) 35 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (2/9) * (90 – x) litres. The equation can be set up as follows:
(2/9) * (90 – x) / (90 – x + x) = 1/4
Solving for x, we get x = 25 litres.
Therefore, the answer is (b) 25 litres.
Question: A mixture contains alcohol and water in the ratio 1:4. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 1:3?
a) 1/4
b) 2/7
c) 3/8
d) 4/9
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. The quantity of alcohol remaining will be (1/5) * (100 – x) litres. The equation can be set up as follows:
(1/5) * (100 – x) / (100 – x + x) = 1/3
Solving for x, we get x = 2/7.
Therefore, the answer is (b) 2/7.
Question: A container contains 70 litres of a mixture of milk and water in the ratio 3:5. How much of the mixture should be taken out and replaced with milk to make the ratio 2:3?
a) 10 litres
b) 12 litres
c) 15 litres
d) 20 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (3/8) * (70 – x) litres. The equation can be set up as follows:
(3/8) * (70 – x) / (70 – x + x) = 2/3
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 2:7. How much of the mixture should be drawn off and replaced with water to make the ratio 1:3?
a) 1/4
b) 2/7
c) 3/8
d) 4/9
Solution: Let’s assume x litres of the mixture is drawn off and replaced with water. The quantity of alcohol remaining will be (2/9) * (100 – x) litres. The equation can be set up as follows:
(2/9) * (100 – x) / (100 – x + x) = 1/3
Solving for x, we get x = 4/9.
Therefore, the answer is (d) 4/9.
Question: A container contains 80 litres of a mixture of milk and water in the ratio 1:3. How much of the mixture should be taken out and replaced with milk to make the ratio 2:5?
a) 18 litres
b) 20 litres
c) 25 litres
d) 30 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (1/4) * (80 – x) litres. The equation can be set up as follows:
(1/4) * (80 – x) / (80 – x + x) = 2/5
Solving for x, we get x = 18 litres.
Therefore, the answer is (a) 18 litres.
Question: A mixture contains alcohol and water in the ratio 3:8. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 2:5?
a) 3/8
b) 4/9
c) 5/11
d) 6/13
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. The quantity of alcohol remaining will be (3/11) * (100 – x) litres. The equation can be set up as follows:
(3/11) * (100 – x) / (100 – x + x) = 2/5
Solving for x, we get x = 5/11.
Therefore, the answer is (c) 5/11.
Question: A container contains 90 litres of a mixture of milk and water in the ratio 2:7. How much of the mixture should be taken out and replaced with milk to make the ratio 1:4?
a) 20 litres
b) 25 litres
c) 30 litres
d) 35 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (2/9) * (90 – x) litres. The equation can be set up as follows:
(2/9) * (90 – x) / (90 – x + x) = 1/4
Solving for x, we get x = 25 litres.
Therefore, the answer is (b) 25 litres.
Question: A mixture contains alcohol and water in the ratio 1:4. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 1:3?
a) 1/4
b) 2/7
c) 3/8
d) 4/9
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. The quantity of alcohol remaining will be (1/5) * (100 – x) litres. The equation can be set up as follows:
(1/5) * (100 – x) / (100 – x + x) = 1/3
Solving for x, we get x = 2/7.
Therefore, the answer is (b) 2/7.
Question: A container contains 70 litres of a mixture of milk and water in the ratio 3:5. How much of the mixture should be taken out and replaced with milk to make the ratio 2:3?
a) 10 litres
b) 12 litres
c) 15 litres
d) 20 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (3/8) * (70 – x) litres. The equation can be set up as follows:
(3/8) * (70 – x) / (70 – x + x) = 2/3
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 2:7. How much of the mixture should be drawn off and replaced with water to make the ratio 1:3?
a) 1/4
b) 2/7
c) 3/8
d) 4/9
Solution: Let’s assume x litres of the mixture is drawn off and replaced with water. The quantity of alcohol remaining will be (2/9) * (100 – x) litres. The equation can be set up as follows:
(2/9) * (100 – x) / (100 – x + x) = 1/3
Solving for x, we get x = 4/9.
Therefore, the answer is (d) 4/9.
Question: A container contains 80 litres of a mixture of milk and water in the ratio 1:3. How much of the mixture should be taken out and replaced with milk to make the ratio 2:5?
a) 18 litres
b) 20 litres
c) 25 litres
d) 30 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (1/4) * (80 – x) litres. The equation can be set up as follows:
(1/4) * (80 – x) / (80 – x + x) = 2/5
Solving for x, we get x = 18 litres.
Therefore, the answer is (a) 18 litres.
Question: A mixture contains alcohol and water in the ratio 3:8. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 2:5?
a) 3/8
b) 4/9
c) 5/11
d) 6/13
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. The quantity of alcohol remaining will be (3/11) * (100 – x) litres. The equation can be set up as follows:
(3/11) * (100 – x) / (100 – x + x) = 2/5
Solving for x, we get x = 5/11.
Therefore, the answer is (c) 5/11.
Question: A container contains 90 litres of a mixture of milk and water in the ratio 2:7. How much of the mixture should be taken out and replaced with milk to make the ratio 1:4?
a) 20 litres
b) 25 litres
c) 30 litres
d) 35 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (2/9) * (90 – x) litres. The equation can be set up as follows:
(2/9) * (90 – x) / (90 – x + x) = 1/4
Solving for x, we get x = 25 litres.
Therefore, the answer is (b) 25 litres.
Question: A mixture contains alcohol and water in the ratio 1:4. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 1:3?
a) 1/4
b) 2/7
c) 3/8
d) 4/9
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. The quantity of alcohol remaining will be (1/5) * (100 – x) litres. The equation can be set up as follows:
(1/5) * (100 – x) / (100 – x + x) = 1/3
Solving for x, we get x = 2/7.
Therefore, the answer is (b) 2/7.
Question: A container contains 70 litres of a mixture of milk and water in the ratio 3:5. How much of the mixture should be taken out and replaced with milk to make the ratio 2:3?
a) 10 litres
b) 12 litres
c) 15 litres
d) 20 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (3/8) * (70 – x) litres. The equation can be set up as follows:
(3/8) * (70 – x) / (70 – x + x) = 2/3
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 2:7. How much of the mixture should be drawn off and replaced with water to make the ratio 1:3?
a) 1/4
b) 2/7
c) 3/8
d) 4/9
Solution: Let’s assume x litres of the mixture is drawn off and replaced with water. The quantity of alcohol remaining will be (2/9) * (100 – x) litres. The equation can be set up as follows:
(2/9) * (100 – x) / (100 – x + x) = 1/3
Solving for x, we get x = 4/9.
Therefore, the answer is (d) 4/9.
Question: A container contains 80 litres of a mixture of milk and water in the ratio 1:3. How much of the mixture should be taken out and replaced with milk to make the ratio 2:5?
a) 18 litres
b) 20 litres
c) 25 litres
d) 30 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (1/4) * (80 – x) litres. The equation can be set up as follows:
(1/4) * (80 – x) / (80 – x + x) = 2/5
Solving for x, we get x = 18 litres.
Therefore, the answer is (a) 18 litres.
Question: A mixture contains alcohol and water in the ratio 3:8. How much of the mixture should be drawn off and replaced with alcohol to make the ratio 2:5?
a) 3/8
b) 4/9
c) 5/11
d) 6/13
Solution: Let’s assume x litres of the mixture is drawn off and replaced with alcohol. The quantity of alcohol remaining will be (3/11) * (100 – x) litres. The equation can be set up as follows:
(3/11) * (100 – x) / (100 – x + x) = 2/5
Solving for x, we get x = 5/11.
Therefore, the answer is (c) 5/11.
Question: A container contains 90 litres of a mixture of milk and water in the ratio 2:7. How much of the mixture should be taken out and replaced with milk to make the ratio 1:4?
a) 20 litres
b) 25 litres
c) 30 litres
d) 35 litres
Solution: Let’s assume x litres of the mixture is taken out and replaced with milk. The quantity of milk remaining will be (2/9) * (90 – x) litres. The equation can be set up as follows:
(2/9) * (90 – x) / (90 – x + x) = 1/4
Solving for x, we get x = 25 litres.
Therefore, the answer is (b) 25 litres.
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