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Three numbers are in the ratio 1:2:3 and their HCF is 12.the numbers are?
- a)4, 8, 12
- b)5, 10, 15
- c)10, 20, 30
- d)12, 24, 36
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Three numbers are in the ratio 1:2:3 and their HCF is 12.the numbers a...
Let the three numbers be x , 2x and 3x.
HCF of these numbers = 12
This means 12 is the common factor (highest) of the three numbers.
So check in the options if all the numbers are divisible by 12 and that option is d) 12,24,36
HCF of these numbers = 12
This means 12 is the common factor (highest) of the three numbers.
So check in the options if all the numbers are divisible by 12 and that option is d) 12,24,36
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Three numbers are in the ratio 1:2:3 and their HCF is 12.the numbers a...
Understanding the Problem
To find three numbers in the ratio 1:2:3 with a given Highest Common Factor (HCF) of 12, we start by defining the numbers based on the ratio.
Defining the Numbers
- Let the three numbers be \( x, 2x, \) and \( 3x \).
- Since the HCF of these numbers is 12, we have \( x = 12 \).
Calculating the Numbers
- Therefore, the numbers can be calculated as follows:
- First number: \( x = 12 \)
- Second number: \( 2x = 2 \times 12 = 24 \)
- Third number: \( 3x = 3 \times 12 = 36 \)
Final Numbers
- The three numbers are:
- \( 12 \)
- \( 24 \)
- \( 36 \)
Verifying the HCF
- To confirm that the HCF is indeed 12:
- Factors of 12: \( 1, 2, 3, 4, 6, 12 \)
- Factors of 24: \( 1, 2, 3, 4, 6, 8, 12, 24 \)
- Factors of 36: \( 1, 2, 3, 4, 6, 9, 12, 18, 36 \)
- The common factors are \( 1, 2, 3, 4, 6, 12 \), confirming that the HCF is 12.
Conclusion
- Thus, the correct answer is option 'D': 12, 24, 36.
To find three numbers in the ratio 1:2:3 with a given Highest Common Factor (HCF) of 12, we start by defining the numbers based on the ratio.
Defining the Numbers
- Let the three numbers be \( x, 2x, \) and \( 3x \).
- Since the HCF of these numbers is 12, we have \( x = 12 \).
Calculating the Numbers
- Therefore, the numbers can be calculated as follows:
- First number: \( x = 12 \)
- Second number: \( 2x = 2 \times 12 = 24 \)
- Third number: \( 3x = 3 \times 12 = 36 \)
Final Numbers
- The three numbers are:
- \( 12 \)
- \( 24 \)
- \( 36 \)
Verifying the HCF
- To confirm that the HCF is indeed 12:
- Factors of 12: \( 1, 2, 3, 4, 6, 12 \)
- Factors of 24: \( 1, 2, 3, 4, 6, 8, 12, 24 \)
- Factors of 36: \( 1, 2, 3, 4, 6, 9, 12, 18, 36 \)
- The common factors are \( 1, 2, 3, 4, 6, 12 \), confirming that the HCF is 12.
Conclusion
- Thus, the correct answer is option 'D': 12, 24, 36.
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Three numbers are in the ratio 1:2:3 and their HCF is 12.the numbers are?a)4, 8, 12 b)5, 10, 15c)10, 20, 30 d)12, 24, 36Correct answer is option 'D'. Can you explain this answer?
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Three numbers are in the ratio 1:2:3 and their HCF is 12.the numbers are?a)4, 8, 12 b)5, 10, 15c)10, 20, 30 d)12, 24, 36Correct answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Three numbers are in the ratio 1:2:3 and their HCF is 12.the numbers are?a)4, 8, 12 b)5, 10, 15c)10, 20, 30 d)12, 24, 36Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three numbers are in the ratio 1:2:3 and their HCF is 12.the numbers are?a)4, 8, 12 b)5, 10, 15c)10, 20, 30 d)12, 24, 36Correct answer is option 'D'. Can you explain this answer?.
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