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If the mean of two numbers is 30 and Geometric Mean is 24 then what will be those two numbers?
- a)36 and 24
- b)30 and 30
- c)48 and 12
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If the mean of two numbers is 30 and Geometric Mean is 24 then what wi...
Let the numbers be x and y.
(x+y)/2 = 30 …(1)
(xy)^1/2 = 24 …(2)
Squaring (2) to get xy = 576, or y = 576/x …(3)
(1) becomes, x + y = 60 …(4)
Put the value of y from (3) in (4) to get
x + 576/x = 60, or
x^2 - 60x + 576 = 0, or
(x-12)(x-48) = 0
or x = 12 or 48 and the corresponding value of y = 48 or 12.
The numbers are 12 and 48.
Most Upvoted Answer
If the mean of two numbers is 30 and Geometric Mean is 24 then what wi...
Solution:
Let the two numbers be x and y.
Given, Mean of two numbers = 30
∴ (x+y)/2 = 30
⇒ x + y = 60
Geometric Mean of two numbers = 24
⇒ √xy = 24
⇒ xy = 576
Substituting the value of xy in the equation x+y = 60, we get
x+y = 60
xy = 576
Let's solve this system of equations using substitution method.
x = 60 - y
Substituting this equation in xy = 576, we get
(60 - y)y = 576
⇒ 60y - y² = 576
⇒ y² - 60y + 576 = 0
⇒ (y - 48)(y - 12) = 0
⇒ y = 48 or y = 12
If y = 48, then x = 60 - y = 12
If y = 12, then x = 60 - y = 48
Therefore, the two numbers are 48 and 12, which is option (C).
Let the two numbers be x and y.
Given, Mean of two numbers = 30
∴ (x+y)/2 = 30
⇒ x + y = 60
Geometric Mean of two numbers = 24
⇒ √xy = 24
⇒ xy = 576
Substituting the value of xy in the equation x+y = 60, we get
x+y = 60
xy = 576
Let's solve this system of equations using substitution method.
x = 60 - y
Substituting this equation in xy = 576, we get
(60 - y)y = 576
⇒ 60y - y² = 576
⇒ y² - 60y + 576 = 0
⇒ (y - 48)(y - 12) = 0
⇒ y = 48 or y = 12
If y = 48, then x = 60 - y = 12
If y = 12, then x = 60 - y = 48
Therefore, the two numbers are 48 and 12, which is option (C).
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If the mean of two numbers is 30 and Geometric Mean is 24 then what will be those two numbers?a)36 and 24b)30 and 30c)48 and 12d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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If the mean of two numbers is 30 and Geometric Mean is 24 then what will be those two numbers?a)36 and 24b)30 and 30c)48 and 12d)None of theseCorrect answer is option 'C'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the mean of two numbers is 30 and Geometric Mean is 24 then what will be those two numbers?a)36 and 24b)30 and 30c)48 and 12d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the mean of two numbers is 30 and Geometric Mean is 24 then what will be those two numbers?a)36 and 24b)30 and 30c)48 and 12d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
If the mean of two numbers is 30 and Geometric Mean is 24 then what will be those two numbers?a)36 and 24b)30 and 30c)48 and 12d)None of theseCorrect answer is option 'C'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the mean of two numbers is 30 and Geometric Mean is 24 then what will be those two numbers?a)36 and 24b)30 and 30c)48 and 12d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the mean of two numbers is 30 and Geometric Mean is 24 then what will be those two numbers?a)36 and 24b)30 and 30c)48 and 12d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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