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The ratio of spirit and water in the two vessels is 5 : 1 and 3 : 7 respectively. In what ratio the liquid of both the vessels should be mixed such that a new mixture containing half spirit and half water is obtained?
- a)3 : 5
- b)5 : 7
- c)1 : 1
- d)4 : 7
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The ratio of spirit and water in the two vessels is 5 : 1 and 3 : 7 re...
Let x litre of first mixture and y litre of the second mixture are mixed.
Quantity of milk in x litre of first mixture = 5x/6
Quantity of milk in y litre of second mixture = 3y/10
Total quantity of the resultant mixture = (x + y)
Quantity of milk in (x + y) litre of the resultant mixture = (x + y) /2
5x/6 + 3y/10 = (x + y) /2
⇒ (25x + 9y) /30 = (x + y) /2
⇒ 25x + 9y = 15 × (x + y)
⇒ 25x + 9y = 15x + 15y
⇒ 10x = 6y
⇒ x/y = 3/5
∴ required ratio = 3 : 5
Quantity of milk in x litre of first mixture = 5x/6
Quantity of milk in y litre of second mixture = 3y/10
Total quantity of the resultant mixture = (x + y)
Quantity of milk in (x + y) litre of the resultant mixture = (x + y) /2
5x/6 + 3y/10 = (x + y) /2
⇒ (25x + 9y) /30 = (x + y) /2
⇒ 25x + 9y = 15 × (x + y)
⇒ 25x + 9y = 15x + 15y
⇒ 10x = 6y
⇒ x/y = 3/5
∴ required ratio = 3 : 5
Alternative method :
Concentration of spirit in the first mixture = 5/6
Concentration of spirit in the second mixture = 3/10
Concentration of spirit in the resultant mixture = 1/2
By rule of allegation,
Concentration of spirit in the first mixture = 5/6
Concentration of spirit in the second mixture = 3/10
Concentration of spirit in the resultant mixture = 1/2
By rule of allegation,
∴ Required ratio = (1/5) : (1/3) = 3 : 5
Most Upvoted Answer
The ratio of spirit and water in the two vessels is 5 : 1 and 3 : 7 re...
Given information:
- The ratio of spirit and water in the first vessel is 5:1.
- The ratio of spirit and water in the second vessel is 3:7.
To find:
- The ratio in which the liquids from both vessels should be mixed to obtain a new mixture containing half spirit and half water.
Solution:
Let's assume that we have x liters of liquid from the first vessel and y liters of liquid from the second vessel.
Ratio of spirit to water in the first vessel:
- The ratio of spirit to water in the first vessel is 5:1.
- So, the quantity of spirit in x liters of liquid from the first vessel = (5/6)x liters.
- The quantity of water in x liters of liquid from the first vessel = (1/6)x liters.
Ratio of spirit to water in the second vessel:
- The ratio of spirit to water in the second vessel is 3:7.
- So, the quantity of spirit in y liters of liquid from the second vessel = (3/10)y liters.
- The quantity of water in y liters of liquid from the second vessel = (7/10)y liters.
Total spirit and water in the mixture:
- The total quantity of spirit in the mixture = (5/6)x + (3/10)y.
- The total quantity of water in the mixture = (1/6)x + (7/10)y.
Given that the new mixture contains half spirit and half water:
- The ratio of spirit to water in the new mixture is 1:1.
- Therefore, the quantity of spirit in the new mixture = the quantity of water in the new mixture.
Equating the quantities of spirit and water in the mixture:
- (5/6)x + (3/10)y = (1/6)x + (7/10)y
Simplifying the equation:
- (5/6)x - (1/6)x = (7/10)y - (3/10)y
- (4/6)x = (4/10)y
- (2/3)x = (2/5)y
- x/y = (2/3)/(2/5)
- x/y = 5/3
Therefore, the liquids from both vessels should be mixed in the ratio 5:3 to obtain a new mixture containing half spirit and half water. Hence, the correct answer is option A) 5:3.
- The ratio of spirit and water in the first vessel is 5:1.
- The ratio of spirit and water in the second vessel is 3:7.
To find:
- The ratio in which the liquids from both vessels should be mixed to obtain a new mixture containing half spirit and half water.
Solution:
Let's assume that we have x liters of liquid from the first vessel and y liters of liquid from the second vessel.
Ratio of spirit to water in the first vessel:
- The ratio of spirit to water in the first vessel is 5:1.
- So, the quantity of spirit in x liters of liquid from the first vessel = (5/6)x liters.
- The quantity of water in x liters of liquid from the first vessel = (1/6)x liters.
Ratio of spirit to water in the second vessel:
- The ratio of spirit to water in the second vessel is 3:7.
- So, the quantity of spirit in y liters of liquid from the second vessel = (3/10)y liters.
- The quantity of water in y liters of liquid from the second vessel = (7/10)y liters.
Total spirit and water in the mixture:
- The total quantity of spirit in the mixture = (5/6)x + (3/10)y.
- The total quantity of water in the mixture = (1/6)x + (7/10)y.
Given that the new mixture contains half spirit and half water:
- The ratio of spirit to water in the new mixture is 1:1.
- Therefore, the quantity of spirit in the new mixture = the quantity of water in the new mixture.
Equating the quantities of spirit and water in the mixture:
- (5/6)x + (3/10)y = (1/6)x + (7/10)y
Simplifying the equation:
- (5/6)x - (1/6)x = (7/10)y - (3/10)y
- (4/6)x = (4/10)y
- (2/3)x = (2/5)y
- x/y = (2/3)/(2/5)
- x/y = 5/3
Therefore, the liquids from both vessels should be mixed in the ratio 5:3 to obtain a new mixture containing half spirit and half water. Hence, the correct answer is option A) 5:3.
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The ratio of spirit and water in the two vessels is 5 : 1 and 3 : 7 respectively. In what ratio the liquid of both the vessels should be mixed such that a new mixture containing half spirit and half water is obtained?a)3 : 5b)5 : 7c)1 : 1d)4 : 7Correct answer is option 'A'. Can you explain this answer?
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