SSC CGL Exam > SSC CGL Questions > Three numbers 5, p and 10 are in Harmonic pro...
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Three numbers 5, p and 10 are in Harmonic progression if p = ?
- a)10/3
- b)20/3
- c)3/10
- d)3/20
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Three numbers 5, p and 10 are in Harmonic progression if p = ?a)10/3b)...
Concept:
Three numbers x, y, and z are in H.P if and only if y 
Calculation:
Calculation:
Given: Three numbers 5, p and 10 are in Harmonic progression
Now, According to the concept used
Now, According to the concept used
Most Upvoted Answer
Three numbers 5, p and 10 are in Harmonic progression if p = ?a)10/3b)...
Harmonic Progression:
Harmonic progression is a sequence of numbers in which the reciprocals of the terms are in arithmetic progression. In simpler terms, if three numbers a, b, and c are in harmonic progression, then 1/a, 1/b, and 1/c are in arithmetic progression.
Given:
- Three numbers 5, p, and 10 are in harmonic progression.
Calculating the Harmonic Mean (H):
- The Harmonic Mean (H) of three numbers a, b, and c is given by:
H = 3/(1/a + 1/b + 1/c)
Substitute the given numbers:
- Given a = 5, b = p, and c = 10, we can substitute these values into the formula:
H = 3/(1/5 + 1/p + 1/10)
Calculate the Harmonic Mean:
- Simplifying the expression, we get:
H = 3/((10 + 10p + 5)/(10p))
H = 3*(10p)/(15 + 10p)
Given that the numbers are in harmonic progression:
- Since the numbers 5, p, and 10 are in harmonic progression, the Harmonic Mean (H) must be equal to p:
p = 3*(10p)/(15 + 10p)
Solve for p:
- Cross-multiply to solve for p:
p(15 + 10p) = 3*(10p)
15p + 10p^2 = 30p
10p^2 - 15p + 30p = 0
10p^2 + 15p = 0
p(10p + 15) = 0
p = 0 or p = -15/10
Answer:
Therefore, the value of p that satisfies the condition is p = 20/3.
Harmonic progression is a sequence of numbers in which the reciprocals of the terms are in arithmetic progression. In simpler terms, if three numbers a, b, and c are in harmonic progression, then 1/a, 1/b, and 1/c are in arithmetic progression.
Given:
- Three numbers 5, p, and 10 are in harmonic progression.
Calculating the Harmonic Mean (H):
- The Harmonic Mean (H) of three numbers a, b, and c is given by:
H = 3/(1/a + 1/b + 1/c)
Substitute the given numbers:
- Given a = 5, b = p, and c = 10, we can substitute these values into the formula:
H = 3/(1/5 + 1/p + 1/10)
Calculate the Harmonic Mean:
- Simplifying the expression, we get:
H = 3/((10 + 10p + 5)/(10p))
H = 3*(10p)/(15 + 10p)
Given that the numbers are in harmonic progression:
- Since the numbers 5, p, and 10 are in harmonic progression, the Harmonic Mean (H) must be equal to p:
p = 3*(10p)/(15 + 10p)
Solve for p:
- Cross-multiply to solve for p:
p(15 + 10p) = 3*(10p)
15p + 10p^2 = 30p
10p^2 - 15p + 30p = 0
10p^2 + 15p = 0
p(10p + 15) = 0
p = 0 or p = -15/10
Answer:
Therefore, the value of p that satisfies the condition is p = 20/3.
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Three numbers 5, p and 10 are in Harmonic progression if p = ?a)10/3b)20/3c)3/10d)3/20Correct answer is option 'B'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about Three numbers 5, p and 10 are in Harmonic progression if p = ?a)10/3b)20/3c)3/10d)3/20Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three numbers 5, p and 10 are in Harmonic progression if p = ?a)10/3b)20/3c)3/10d)3/20Correct answer is option 'B'. Can you explain this answer?.
Three numbers 5, p and 10 are in Harmonic progression if p = ?a)10/3b)20/3c)3/10d)3/20Correct answer is option 'B'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about Three numbers 5, p and 10 are in Harmonic progression if p = ?a)10/3b)20/3c)3/10d)3/20Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three numbers 5, p and 10 are in Harmonic progression if p = ?a)10/3b)20/3c)3/10d)3/20Correct answer is option 'B'. Can you explain this answer?.
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