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Divide 69 into three parts such that which are in A.P. and such that the product of first two parts is 460?
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Divide 69 into three parts such that which are in A.P. and such that t...
Given:
- The number to be divided is 69
- The parts are in arithmetic progression (A.P.)
- The product of the first two parts is 460
Let the three parts be:
- First part: a - d
- Second part: a
- Third part: a + d
Calculating the parts:
- Let the common difference be d
- The sum of the three parts is 69
- Therefore, a - d + a + a + d = 69
- Simplifying, we get 3a = 69
- So, a = 23
Product of the first two parts:
- The product of the first two parts is 460
- So, (a - d) * a = 460
- Substituting the value of a, we get (23 - d) * 23 = 460
- Solving further, we get d = 7
Therefore, the three parts are:
- First part: 23 - 7 = 16
- Second part: 23
- Third part: 23 + 7 = 30
Verification:
- The sum of the three parts is 16 + 23 + 30 = 69
- The product of the first two parts is 16 * 23 = 460
Conclusion:
- Hence, the three parts of 69 which are in arithmetic progression and have a product of 460 are 16, 23, and 30.
- The number to be divided is 69
- The parts are in arithmetic progression (A.P.)
- The product of the first two parts is 460
Let the three parts be:
- First part: a - d
- Second part: a
- Third part: a + d
Calculating the parts:
- Let the common difference be d
- The sum of the three parts is 69
- Therefore, a - d + a + a + d = 69
- Simplifying, we get 3a = 69
- So, a = 23
Product of the first two parts:
- The product of the first two parts is 460
- So, (a - d) * a = 460
- Substituting the value of a, we get (23 - d) * 23 = 460
- Solving further, we get d = 7
Therefore, the three parts are:
- First part: 23 - 7 = 16
- Second part: 23
- Third part: 23 + 7 = 30
Verification:
- The sum of the three parts is 16 + 23 + 30 = 69
- The product of the first two parts is 16 * 23 = 460
Conclusion:
- Hence, the three parts of 69 which are in arithmetic progression and have a product of 460 are 16, 23, and 30.
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Divide 69 into three parts such that which are in A.P. and such that the product of first two parts is 460?
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Divide 69 into three parts such that which are in A.P. and such that the product of first two parts is 460? 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 Divide 69 into three parts such that which are in A.P. and such that the product of first two parts is 460? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Divide 69 into three parts such that which are in A.P. and such that the product of first two parts is 460?.
Divide 69 into three parts such that which are in A.P. and such that the product of first two parts is 460? 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 Divide 69 into three parts such that which are in A.P. and such that the product of first two parts is 460? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Divide 69 into three parts such that which are in A.P. and such that the product of first two parts is 460?.
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