UPSC Exam > UPSC Questions > The percentage volumes of brandy in three sol...
Start Learning for Free
The percentage volumes of brandy in three solutions X, Y and Z form a geometric progression in that order. If we mix the first, second and third solutions in the ratio 1/6: 1/4: 1/3, by volume, we obtain a solution containing 48% brandy. If we mix them in the ratio 1/2:1/3:1/6, by volume, we obtain a solution containing 33% brandy. What is the percentage of brandy in solution Y?
- a)24%
- b)30%
- c)36%
- d)42%
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The percentage volumes of brandy in three solutions X, Y and Z form a ...
Let percentage of brandy in solutions X, Y and Z be a, ar and ar2 respectively (‘a’ being the first term and ‘r’ the common ratio of the geometric progression).
In the first case, we mix the solutions in the ratio 1/6: 1/4: 1/3, i.e. 1/6 x12, 1/4 x12, 1/3 ×12 [LCM(6,4,3) = 12]
= 2: 3: 4.
In the second case, we mix the solutions in the ratio 1/2: 1/3: 1/6, i.e. 1/2 ×6, 1/3 x6, 1/6 ×6 = 3: 2: 1.
So, [(2(a/100)+3(ar/100)+4(ar2)/100)/(2+3+4)]x100 = 48
⇒ 2a + 3ar + 4ar2 = 48x9………….І
And [{3(a/100)+2(ar/100)+(ar2/100)}/(3+2+1)]×100 = 33
⇒ 3a + 2ar + ar2 = 33×6……….ІІ
Dividing І by ІІ, we get:
4r2 – 3r – 10 = 0
⇒ r = 2, or r = - 5/4 (negative value of ‘r’ will yield in negative quantity and percentage of brandy, so not acceptable here).
Putting the value of r (=2) in either І or ІІ will yield, a = 18.
So, percentage of brandy in solution Y = ar = 18×2 = 36%
In the first case, we mix the solutions in the ratio 1/6: 1/4: 1/3, i.e. 1/6 x12, 1/4 x12, 1/3 ×12 [LCM(6,4,3) = 12]
= 2: 3: 4.
In the second case, we mix the solutions in the ratio 1/2: 1/3: 1/6, i.e. 1/2 ×6, 1/3 x6, 1/6 ×6 = 3: 2: 1.
So, [(2(a/100)+3(ar/100)+4(ar2)/100)/(2+3+4)]x100 = 48
⇒ 2a + 3ar + 4ar2 = 48x9………….І
And [{3(a/100)+2(ar/100)+(ar2/100)}/(3+2+1)]×100 = 33
⇒ 3a + 2ar + ar2 = 33×6……….ІІ
Dividing І by ІІ, we get:
4r2 – 3r – 10 = 0
⇒ r = 2, or r = - 5/4 (negative value of ‘r’ will yield in negative quantity and percentage of brandy, so not acceptable here).
Putting the value of r (=2) in either І or ІІ will yield, a = 18.
So, percentage of brandy in solution Y = ar = 18×2 = 36%
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
The percentage volumes of brandy in three solutions X, Y and Z form a geometric progression in that order. If we mix the first, second and third solutions in the ratio 1/6: 1/4: 1/3, by volume, we obtain a solution containing 48% brandy. If we mix them in the ratio 1/2:1/3:1/6, by volume, we obtain a solution containing 33% brandy. What is the percentage of brandy in solution Y?a)24%b)30%c)36%d)42%Correct answer is option 'C'. Can you explain this answer?
Question Description
The percentage volumes of brandy in three solutions X, Y and Z form a geometric progression in that order. If we mix the first, second and third solutions in the ratio 1/6: 1/4: 1/3, by volume, we obtain a solution containing 48% brandy. If we mix them in the ratio 1/2:1/3:1/6, by volume, we obtain a solution containing 33% brandy. What is the percentage of brandy in solution Y?a)24%b)30%c)36%d)42%Correct answer is option 'C'. 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 The percentage volumes of brandy in three solutions X, Y and Z form a geometric progression in that order. If we mix the first, second and third solutions in the ratio 1/6: 1/4: 1/3, by volume, we obtain a solution containing 48% brandy. If we mix them in the ratio 1/2:1/3:1/6, by volume, we obtain a solution containing 33% brandy. What is the percentage of brandy in solution Y?a)24%b)30%c)36%d)42%Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The percentage volumes of brandy in three solutions X, Y and Z form a geometric progression in that order. If we mix the first, second and third solutions in the ratio 1/6: 1/4: 1/3, by volume, we obtain a solution containing 48% brandy. If we mix them in the ratio 1/2:1/3:1/6, by volume, we obtain a solution containing 33% brandy. What is the percentage of brandy in solution Y?a)24%b)30%c)36%d)42%Correct answer is option 'C'. Can you explain this answer?.
The percentage volumes of brandy in three solutions X, Y and Z form a geometric progression in that order. If we mix the first, second and third solutions in the ratio 1/6: 1/4: 1/3, by volume, we obtain a solution containing 48% brandy. If we mix them in the ratio 1/2:1/3:1/6, by volume, we obtain a solution containing 33% brandy. What is the percentage of brandy in solution Y?a)24%b)30%c)36%d)42%Correct answer is option 'C'. 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 The percentage volumes of brandy in three solutions X, Y and Z form a geometric progression in that order. If we mix the first, second and third solutions in the ratio 1/6: 1/4: 1/3, by volume, we obtain a solution containing 48% brandy. If we mix them in the ratio 1/2:1/3:1/6, by volume, we obtain a solution containing 33% brandy. What is the percentage of brandy in solution Y?a)24%b)30%c)36%d)42%Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The percentage volumes of brandy in three solutions X, Y and Z form a geometric progression in that order. If we mix the first, second and third solutions in the ratio 1/6: 1/4: 1/3, by volume, we obtain a solution containing 48% brandy. If we mix them in the ratio 1/2:1/3:1/6, by volume, we obtain a solution containing 33% brandy. What is the percentage of brandy in solution Y?a)24%b)30%c)36%d)42%Correct answer is option 'C'. Can you explain this answer?.
Solutions for The percentage volumes of brandy in three solutions X, Y and Z form a geometric progression in that order. If we mix the first, second and third solutions in the ratio 1/6: 1/4: 1/3, by volume, we obtain a solution containing 48% brandy. If we mix them in the ratio 1/2:1/3:1/6, by volume, we obtain a solution containing 33% brandy. What is the percentage of brandy in solution Y?a)24%b)30%c)36%d)42%Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of The percentage volumes of brandy in three solutions X, Y and Z form a geometric progression in that order. If we mix the first, second and third solutions in the ratio 1/6: 1/4: 1/3, by volume, we obtain a solution containing 48% brandy. If we mix them in the ratio 1/2:1/3:1/6, by volume, we obtain a solution containing 33% brandy. What is the percentage of brandy in solution Y?a)24%b)30%c)36%d)42%Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The percentage volumes of brandy in three solutions X, Y and Z form a geometric progression in that order. If we mix the first, second and third solutions in the ratio 1/6: 1/4: 1/3, by volume, we obtain a solution containing 48% brandy. If we mix them in the ratio 1/2:1/3:1/6, by volume, we obtain a solution containing 33% brandy. What is the percentage of brandy in solution Y?a)24%b)30%c)36%d)42%Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The percentage volumes of brandy in three solutions X, Y and Z form a geometric progression in that order. If we mix the first, second and third solutions in the ratio 1/6: 1/4: 1/3, by volume, we obtain a solution containing 48% brandy. If we mix them in the ratio 1/2:1/3:1/6, by volume, we obtain a solution containing 33% brandy. What is the percentage of brandy in solution Y?a)24%b)30%c)36%d)42%Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The percentage volumes of brandy in three solutions X, Y and Z form a geometric progression in that order. If we mix the first, second and third solutions in the ratio 1/6: 1/4: 1/3, by volume, we obtain a solution containing 48% brandy. If we mix them in the ratio 1/2:1/3:1/6, by volume, we obtain a solution containing 33% brandy. What is the percentage of brandy in solution Y?a)24%b)30%c)36%d)42%Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The percentage volumes of brandy in three solutions X, Y and Z form a geometric progression in that order. If we mix the first, second and third solutions in the ratio 1/6: 1/4: 1/3, by volume, we obtain a solution containing 48% brandy. If we mix them in the ratio 1/2:1/3:1/6, by volume, we obtain a solution containing 33% brandy. What is the percentage of brandy in solution Y?a)24%b)30%c)36%d)42%Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup