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Two equal vessels A and B contain 60% of sugar and 40% of sugar respectively and the remaining Rava. In which 40 litres of mixture is taken out from vessel A and replaced into vessel B. Find the initial quantity of vessel if the final ratio of sugar and Rava in vessel B is 16 : 19 ?
- a)80 litres
- b)100 litres
- c)120 litres
- d)90 litres
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two equal vessels A and B contain 60% of sugar and 40% of sugar respec...
Vessel A Sugar and Rava ratio = 3 : 2 Vessel B sugar and Rava ratio = 2 : 3
Given,
In vessel A (3/5 x 40 = 24) (2/5 x 40 = 16)
(2x + 24)/(3x + 16) = 16/19
38x + 456 = 48x + 256
10x= 200
x = 20 litres
Initial quantity = x*5 = 100 litres
Most Upvoted Answer
Two equal vessels A and B contain 60% of sugar and 40% of sugar respec...
Problem Statement:
Two equal vessels A and B contain 60% of sugar and 40% of sugar respectively and the remaining Rava. In which 40 litres of mixture is taken out from vessel A and replaced into vessel B. Find the initial quantity of vessel if the final ratio of sugar and Rava in vessel B is 16 : 19?
Solution:
Let the initial quantity of each vessel be x litres.
Quantity of sugar in vessel A = 60% of x = 0.6x
Quantity of sugar in vessel B = 40% of x = 0.4x
Let 40 litres of the mixture be taken out from vessel A.
After taking out 40 litres of mixture from vessel A, the quantity of sugar in vessel A = 0.6x - (0.6x × 40/100) = 0.36x
After adding the same 40 litres of mixture into vessel B, the quantity of sugar in vessel B = 0.4x + (0.6x × 40/100) = 0.64x
Let the final quantity of mixture in vessel B be y litres.
Given that the final ratio of sugar and Rava in vessel B is 16 : 19.
Therefore, the quantity of sugar in vessel B = (16/35) y
And the quantity of Rava in vessel B = (19/35) y
Equating the quantity of sugar in vessel B, we get:
0.64x = (16/35) y
Simplifying the above equation, we get:
y = (35 × 0.64x)/16 = 1.4x
Equating the quantity of Rava in vessel B, we get:
(19/35) y = (60/100) × x + (40/100) × (y - x)
Simplifying the above equation, we get:
19y = 54x + 40y - 40x
Solving for y, we get:
y = (14/19) x
Substituting the value of y in terms of x, we get:
(14/19) x = 1.4x
Solving for x, we get:
x = 100 litres
Therefore, the initial quantity of each vessel is 100 litres.
Two equal vessels A and B contain 60% of sugar and 40% of sugar respectively and the remaining Rava. In which 40 litres of mixture is taken out from vessel A and replaced into vessel B. Find the initial quantity of vessel if the final ratio of sugar and Rava in vessel B is 16 : 19?
Solution:
Let the initial quantity of each vessel be x litres.
Quantity of sugar in vessel A = 60% of x = 0.6x
Quantity of sugar in vessel B = 40% of x = 0.4x
Let 40 litres of the mixture be taken out from vessel A.
After taking out 40 litres of mixture from vessel A, the quantity of sugar in vessel A = 0.6x - (0.6x × 40/100) = 0.36x
After adding the same 40 litres of mixture into vessel B, the quantity of sugar in vessel B = 0.4x + (0.6x × 40/100) = 0.64x
Let the final quantity of mixture in vessel B be y litres.
Given that the final ratio of sugar and Rava in vessel B is 16 : 19.
Therefore, the quantity of sugar in vessel B = (16/35) y
And the quantity of Rava in vessel B = (19/35) y
Equating the quantity of sugar in vessel B, we get:
0.64x = (16/35) y
Simplifying the above equation, we get:
y = (35 × 0.64x)/16 = 1.4x
Equating the quantity of Rava in vessel B, we get:
(19/35) y = (60/100) × x + (40/100) × (y - x)
Simplifying the above equation, we get:
19y = 54x + 40y - 40x
Solving for y, we get:
y = (14/19) x
Substituting the value of y in terms of x, we get:
(14/19) x = 1.4x
Solving for x, we get:
x = 100 litres
Therefore, the initial quantity of each vessel is 100 litres.
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Two equal vessels A and B contain 60% of sugar and 40% of sugar respectively and the remaining Rava. In which 40 litres of mixture is taken out from vessel A and replaced into vessel B. Find the initial quantity of vessel if the final ratio of sugar and Rava in vessel B is 16 : 19 ?a)80 litresb)100 litresc)120 litresd)90 litresCorrect answer is option 'B'. Can you explain this answer?
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Two equal vessels A and B contain 60% of sugar and 40% of sugar respectively and the remaining Rava. In which 40 litres of mixture is taken out from vessel A and replaced into vessel B. Find the initial quantity of vessel if the final ratio of sugar and Rava in vessel B is 16 : 19 ?a)80 litresb)100 litresc)120 litresd)90 litresCorrect answer is option 'B'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two equal vessels A and B contain 60% of sugar and 40% of sugar respectively and the remaining Rava. In which 40 litres of mixture is taken out from vessel A and replaced into vessel B. Find the initial quantity of vessel if the final ratio of sugar and Rava in vessel B is 16 : 19 ?a)80 litresb)100 litresc)120 litresd)90 litresCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two equal vessels A and B contain 60% of sugar and 40% of sugar respectively and the remaining Rava. In which 40 litres of mixture is taken out from vessel A and replaced into vessel B. Find the initial quantity of vessel if the final ratio of sugar and Rava in vessel B is 16 : 19 ?a)80 litresb)100 litresc)120 litresd)90 litresCorrect answer is option 'B'. Can you explain this answer?.
Two equal vessels A and B contain 60% of sugar and 40% of sugar respectively and the remaining Rava. In which 40 litres of mixture is taken out from vessel A and replaced into vessel B. Find the initial quantity of vessel if the final ratio of sugar and Rava in vessel B is 16 : 19 ?a)80 litresb)100 litresc)120 litresd)90 litresCorrect answer is option 'B'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two equal vessels A and B contain 60% of sugar and 40% of sugar respectively and the remaining Rava. In which 40 litres of mixture is taken out from vessel A and replaced into vessel B. Find the initial quantity of vessel if the final ratio of sugar and Rava in vessel B is 16 : 19 ?a)80 litresb)100 litresc)120 litresd)90 litresCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two equal vessels A and B contain 60% of sugar and 40% of sugar respectively and the remaining Rava. In which 40 litres of mixture is taken out from vessel A and replaced into vessel B. Find the initial quantity of vessel if the final ratio of sugar and Rava in vessel B is 16 : 19 ?a)80 litresb)100 litresc)120 litresd)90 litresCorrect answer is option 'B'. Can you explain this answer?.
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