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HCF and LCM of two numbers is 5 and 275 respectively and the sum of these two numbers is 80. Find the sum of the reciprocals of these numbers.
- a)15/242
- b)16/275
- c)32/221
- d)20/268
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
HCF and LCM of two numbers is 5 and 275 respectively and the sum of th...
Understanding the Problem
To solve for the two numbers given their HCF, LCM, and sum, we can use the relationship between HCF, LCM, and the product of the two numbers.
Key Relationships
- HCF (Highest Common Factor) = 5
- LCM (Least Common Multiple) = 275
- Sum of the two numbers = 80
Finding the Product of the Numbers
Using the relationship:
- HCF × LCM = Product of the two numbers
Therefore, we calculate:
- 5 × 275 = 1375
Let the two numbers be x and y. Hence, we have:
- x + y = 80
- xy = 1375
Forming the Quadratic Equation
From the equations, we can form:
- t^2 - (x+y)t + xy = 0
- t^2 - 80t + 1375 = 0
Calculating the Roots
Using the quadratic formula:
- t = [80 ± sqrt((80)^2 - 4 × 1 × 1375)] / 2
Calculating the discriminant:
- (80)^2 - 4 × 1375 = 6400 - 5500 = 900
Thus, we have:
- t = [80 ± 30] / 2
This gives us:
- t = 55 and t = 25
So, the two numbers are 55 and 25.
Finding the Sum of the Reciprocals
The sum of the reciprocals of the numbers is given by:
- (1/x) + (1/y) = (y + x) / (xy)
Substituting the values:
- (55 + 25) / (55 × 25) = 80 / 1375 = 16 / 275
Conclusion
The sum of the reciprocals of the two numbers is:
- 16/275
Thus, the correct answer is option 'B'.
To solve for the two numbers given their HCF, LCM, and sum, we can use the relationship between HCF, LCM, and the product of the two numbers.
Key Relationships
- HCF (Highest Common Factor) = 5
- LCM (Least Common Multiple) = 275
- Sum of the two numbers = 80
Finding the Product of the Numbers
Using the relationship:
- HCF × LCM = Product of the two numbers
Therefore, we calculate:
- 5 × 275 = 1375
Let the two numbers be x and y. Hence, we have:
- x + y = 80
- xy = 1375
Forming the Quadratic Equation
From the equations, we can form:
- t^2 - (x+y)t + xy = 0
- t^2 - 80t + 1375 = 0
Calculating the Roots
Using the quadratic formula:
- t = [80 ± sqrt((80)^2 - 4 × 1 × 1375)] / 2
Calculating the discriminant:
- (80)^2 - 4 × 1375 = 6400 - 5500 = 900
Thus, we have:
- t = [80 ± 30] / 2
This gives us:
- t = 55 and t = 25
So, the two numbers are 55 and 25.
Finding the Sum of the Reciprocals
The sum of the reciprocals of the numbers is given by:
- (1/x) + (1/y) = (y + x) / (xy)
Substituting the values:
- (55 + 25) / (55 × 25) = 80 / 1375 = 16 / 275
Conclusion
The sum of the reciprocals of the two numbers is:
- 16/275
Thus, the correct answer is option 'B'.
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Community Answer
HCF and LCM of two numbers is 5 and 275 respectively and the sum of th...
x + y = 80, xy = 5*275 = 1375
sum of reciprocals = 1/x + 1/y = (x+y)/xy = 80/1375
sum of reciprocals = 1/x + 1/y = (x+y)/xy = 80/1375
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HCF and LCM of two numbers is 5 and 275 respectively and the sum of these two numbers is 80. Find the sum of the reciprocals of these numbers.a)15/242b)16/275c)32/221d)20/268e)None of theseCorrect answer is option 'B'. Can you explain this answer?
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HCF and LCM of two numbers is 5 and 275 respectively and the sum of these two numbers is 80. Find the sum of the reciprocals of these numbers.a)15/242b)16/275c)32/221d)20/268e)None of theseCorrect answer is option 'B'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about HCF and LCM of two numbers is 5 and 275 respectively and the sum of these two numbers is 80. Find the sum of the reciprocals of these numbers.a)15/242b)16/275c)32/221d)20/268e)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for HCF and LCM of two numbers is 5 and 275 respectively and the sum of these two numbers is 80. Find the sum of the reciprocals of these numbers.a)15/242b)16/275c)32/221d)20/268e)None of theseCorrect answer is option 'B'. Can you explain this answer?.
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