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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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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? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about 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? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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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