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Two cans P and Q contains milk and water in the ratio of 3:2 and 7:3 respectively. The ratio in which these two cans be mixed so as to get a new mixture containing milk and water in the ratio 7:4.
- a)4:7
- b)7:3
- c)7:4
- d)7:5
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Two cans P and Q contains milk and water in the ratio of 3:2 and 7:3 r...
Answer – c) 7:4 Explanation : Milk in 1 can = 3/5 and water = 2/5. Similarly in second can milk = 7/10 and water = 3/10.
Take the ratio = K:1 (3k/5 + 7/10)/(2k/5 + 3/10) = 7/4 Solve for k, we get k = 7/4. So the ratio is 7:4
Take the ratio = K:1 (3k/5 + 7/10)/(2k/5 + 3/10) = 7/4 Solve for k, we get k = 7/4. So the ratio is 7:4
Most Upvoted Answer
Two cans P and Q contains milk and water in the ratio of 3:2 and 7:3 r...
Answer – c) 7:4 Explanation : Milk in 1 can = 3/5 and water = 2/5. Similarly in second can milk = 7/10 and water = 3/10.
Take the ratio = K:1 (3k/5 + 7/10)/(2k/5 + 3/10) = 7/4 Solve for k, we get k = 7/4. So the ratio is 7:4
Take the ratio = K:1 (3k/5 + 7/10)/(2k/5 + 3/10) = 7/4 Solve for k, we get k = 7/4. So the ratio is 7:4
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Two cans P and Q contains milk and water in the ratio of 3:2 and 7:3 r...
Given information:
- Can P contains milk and water in the ratio of 3:2.
- Can Q contains milk and water in the ratio of 7:3.
- We need to find the ratio in which cans P and Q should be mixed to obtain a new mixture with a milk-to-water ratio of 7:4.
Let's assume that we mix cans P and Q in the ratio of x:y.
Ratio of milk in the mixture:
- In can P, the ratio of milk to the total mixture is 3:5 (since milk and water are in the ratio of 3:2).
- In can Q, the ratio of milk to the total mixture is 7:10 (since milk and water are in the ratio of 7:3).
Therefore, the ratio of milk in the new mixture is:
(3x + 7y) : (5x + 10y)
Ratio of water in the mixture:
- In can P, the ratio of water to the total mixture is 2:5.
- In can Q, the ratio of water to the total mixture is 3:10.
Therefore, the ratio of water in the new mixture is:
(2x + 3y) : (5x + 10y)
According to the given condition, the ratio of milk to water in the new mixture should be 7:4. So we have the equation:
(3x + 7y) / (2x + 3y) = 7/4
Now, we can solve this equation to find the values of x and y.
Cross-multiplying, we get:
4(3x + 7y) = 7(2x + 3y)
12x + 28y = 14x + 21y
28y - 21y = 14x - 12x
7y = 2x
7/2 = x/y
Therefore, the ratio in which cans P and Q should be mixed to obtain a new mixture with a milk-to-water ratio of 7:4 is 7:2, which can be simplified to 7:4.
- Can P contains milk and water in the ratio of 3:2.
- Can Q contains milk and water in the ratio of 7:3.
- We need to find the ratio in which cans P and Q should be mixed to obtain a new mixture with a milk-to-water ratio of 7:4.
Let's assume that we mix cans P and Q in the ratio of x:y.
Ratio of milk in the mixture:
- In can P, the ratio of milk to the total mixture is 3:5 (since milk and water are in the ratio of 3:2).
- In can Q, the ratio of milk to the total mixture is 7:10 (since milk and water are in the ratio of 7:3).
Therefore, the ratio of milk in the new mixture is:
(3x + 7y) : (5x + 10y)
Ratio of water in the mixture:
- In can P, the ratio of water to the total mixture is 2:5.
- In can Q, the ratio of water to the total mixture is 3:10.
Therefore, the ratio of water in the new mixture is:
(2x + 3y) : (5x + 10y)
According to the given condition, the ratio of milk to water in the new mixture should be 7:4. So we have the equation:
(3x + 7y) / (2x + 3y) = 7/4
Now, we can solve this equation to find the values of x and y.
Cross-multiplying, we get:
4(3x + 7y) = 7(2x + 3y)
12x + 28y = 14x + 21y
28y - 21y = 14x - 12x
7y = 2x
7/2 = x/y
Therefore, the ratio in which cans P and Q should be mixed to obtain a new mixture with a milk-to-water ratio of 7:4 is 7:2, which can be simplified to 7:4.
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