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The sum of two numbers is 14 and their product is 36. What is the sum of the reciprocals of these numbers?
- a)6/17
- b)5/18
- c)7/18
- d)5/19
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The sum of two numbers is 14 and their product is 36. What is the sum...
Sum of two numbers = 14
x + y = 14
product of two numbers = 36
xy = 36
Sum of reciprocals = 1/x + 1/y = x + y /xy = 14/36 = 7/18
View all questions of this test
x + y = 14
product of two numbers = 36
xy = 36
Sum of reciprocals = 1/x + 1/y = x + y /xy = 14/36 = 7/18
Most Upvoted Answer
The sum of two numbers is 14 and their product is 36. What is the sum...
Let's assume the two numbers as x and y.
Given that the sum of the two numbers is 14, we can write the equation as:
x + y = 14
Also, given that the product of the two numbers is 36, we can write the equation as:
xy = 36
To find the sum of the reciprocals of these numbers, we need to find the values of 1/x and 1/y and then add them together.
Let's find the value of x in terms of y from the first equation:
x = 14 - y
Substituting this value of x in the second equation, we get:
(14 - y)y = 36
Expanding the equation, we get:
14y - y^2 = 36
Rearranging the terms, we get a quadratic equation:
y^2 - 14y + 36 = 0
Now we can solve this quadratic equation to find the values of y.
Factoring the equation, we get:
(y - 6)(y - 6) = 0
So, the only possible value for y is 6.
Substituting this value of y in the first equation, we can find the value of x:
x + 6 = 14
x = 14 - 6
x = 8
Therefore, the two numbers are 8 and 6.
Now, let's find the sum of the reciprocals of these numbers:
1/x + 1/y = 1/8 + 1/6
= (6 + 8) / (8 * 6)
= 14 / 48
= 7 / 24
So, the sum of the reciprocals of the two numbers is 7/24.
Therefore, the correct answer is option C) 7/18.
Given that the sum of the two numbers is 14, we can write the equation as:
x + y = 14
Also, given that the product of the two numbers is 36, we can write the equation as:
xy = 36
To find the sum of the reciprocals of these numbers, we need to find the values of 1/x and 1/y and then add them together.
Let's find the value of x in terms of y from the first equation:
x = 14 - y
Substituting this value of x in the second equation, we get:
(14 - y)y = 36
Expanding the equation, we get:
14y - y^2 = 36
Rearranging the terms, we get a quadratic equation:
y^2 - 14y + 36 = 0
Now we can solve this quadratic equation to find the values of y.
Factoring the equation, we get:
(y - 6)(y - 6) = 0
So, the only possible value for y is 6.
Substituting this value of y in the first equation, we can find the value of x:
x + 6 = 14
x = 14 - 6
x = 8
Therefore, the two numbers are 8 and 6.
Now, let's find the sum of the reciprocals of these numbers:
1/x + 1/y = 1/8 + 1/6
= (6 + 8) / (8 * 6)
= 14 / 48
= 7 / 24
So, the sum of the reciprocals of the two numbers is 7/24.
Therefore, the correct answer is option C) 7/18.
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The sum of two numbers is 14 and their product is 36. What is the sum of the reciprocals of these numbers?a)6/17b)5/18c)7/18d)5/19Correct answer is option 'C'. Can you explain this answer?
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The sum of two numbers is 14 and their product is 36. What is the sum of the reciprocals of these numbers?a)6/17b)5/18c)7/18d)5/19Correct 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 sum of two numbers is 14 and their product is 36. What is the sum of the reciprocals of these numbers?a)6/17b)5/18c)7/18d)5/19Correct 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 sum of two numbers is 14 and their product is 36. What is the sum of the reciprocals of these numbers?a)6/17b)5/18c)7/18d)5/19Correct answer is option 'C'. Can you explain this answer?.
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