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A number consisting two digit is four times the sum of its digits and if 27 be added to it the digits are reversed?
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A number consisting two digit is four times the sum of its digits and ...
Given Information:
- Let the two-digit number be represented by 10a + b, where a is the digit in the tens place and b is the digit in the units place.
- The number is four times the sum of its digits: 10a + b = 4(a + b)
- When 27 is added to the number, the digits are reversed: 10a + b + 27 = 10b + a
Equations to solve:
1. 10a + b = 4(a + b)
2. 10a + b + 27 = 10b + a
Solving the equations:
- From equation 1: 10a + b = 4a + 4b
- Rearranging terms: 6a = 3b
- Dividing by 3: 2a = b
- Substituting 2a for b in equation 2:
10a + 2a + 27 = 10(2a) + a
12a + 27 = 20a + a
27 = 19a
a = 27 / 19
a = 1.42
Conclusion:
- Since a should be a whole number, the assumption that the number consists of two digits is incorrect. The number must actually be a single-digit number.
- Therefore, the initial assumption was flawed, and the problem cannot be solved with the given conditions for a two-digit number.
- Let the two-digit number be represented by 10a + b, where a is the digit in the tens place and b is the digit in the units place.
- The number is four times the sum of its digits: 10a + b = 4(a + b)
- When 27 is added to the number, the digits are reversed: 10a + b + 27 = 10b + a
Equations to solve:
1. 10a + b = 4(a + b)
2. 10a + b + 27 = 10b + a
Solving the equations:
- From equation 1: 10a + b = 4a + 4b
- Rearranging terms: 6a = 3b
- Dividing by 3: 2a = b
- Substituting 2a for b in equation 2:
10a + 2a + 27 = 10(2a) + a
12a + 27 = 20a + a
27 = 19a
a = 27 / 19
a = 1.42
Conclusion:
- Since a should be a whole number, the assumption that the number consists of two digits is incorrect. The number must actually be a single-digit number.
- Therefore, the initial assumption was flawed, and the problem cannot be solved with the given conditions for a two-digit number.
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A number consisting two digit is four times the sum of its digits and if 27 be added to it the digits are reversed?
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A number consisting two digit is four times the sum of its digits and if 27 be added to it the digits are reversed? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A number consisting two digit is four times the sum of its digits and if 27 be added to it the digits are reversed? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A number consisting two digit is four times the sum of its digits and if 27 be added to it the digits are reversed?.
A number consisting two digit is four times the sum of its digits and if 27 be added to it the digits are reversed? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A number consisting two digit is four times the sum of its digits and if 27 be added to it the digits are reversed? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A number consisting two digit is four times the sum of its digits and if 27 be added to it the digits are reversed?.
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