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In a two-digit number, if it is known that its unit\'s digit exceeds its ten\'s digit by 2 and that the product of the given number and the sum of its digits is equal to 144,then the number is
- a)46
- b)42
- c)26
- d)24
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In a two-digit number, if it is known that its unit\'s digit exceeds i...
Let the ten's digit be x
Then, unit's digit = x + 2
Number = 10x + (x + 2) = 11x + 2
Sum of digits = x + (x + 2) = 2x + 2
∴ (11x + 2)(2x + 2) = 144
⇒ 22x2 + 26x - 140 = 0
⇒ 11x2 + 13x - 70 = 0
⇒ (x - 2)(11x + 35) = 0
⇒ x = 2
Hence, required number = 11x + 2 = 24.
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Then, unit's digit = x + 2
Number = 10x + (x + 2) = 11x + 2
Sum of digits = x + (x + 2) = 2x + 2
∴ (11x + 2)(2x + 2) = 144
⇒ 22x2 + 26x - 140 = 0
⇒ 11x2 + 13x - 70 = 0
⇒ (x - 2)(11x + 35) = 0
⇒ x = 2
Hence, required number = 11x + 2 = 24.
Most Upvoted Answer
In a two-digit number, if it is known that its unit\'s digit exceeds i...
Given information:
- The unit's digit exceeds the ten's digit by 2.
- The product of the given number and the sum of its digits is equal to 144.
To find:
The two-digit number.
Solution:
Let the ten's digit be x and the unit's digit be x + 2.
The given number can be expressed as 10x + (x + 2).
The sum of the digits can be expressed as x + (x + 2) = 2x + 2.
According to the given condition, the product of the number and the sum of its digits is 144:
(10x + (x + 2))(2x + 2) = 144
Simplifying the equation:
(10x + x + 2)(2x + 2) = 144
(11x + 2)(2x + 2) = 144
Expanding the equation:
22x^2 + 26x + 4 = 144
Rearranging the equation:
22x^2 + 26x - 140 = 0
Dividing the equation by 2:
11x^2 + 13x - 70 = 0
Factoring the quadratic equation:
(11x - 10)(x + 7) = 0
Setting each factor equal to zero and solving for x:
11x - 10 = 0 or x + 7 = 0
11x = 10 or x = -7
x = 10/11 or x = -7
Since the number is a two-digit number, x cannot be a fraction or negative.
Therefore, x = 10/11 is not a valid solution.
Hence, x = -7 is not a valid solution.
Therefore, there is no solution to this equation.
Thus, the given information is inconsistent, and we cannot determine the two-digit number.
- The unit's digit exceeds the ten's digit by 2.
- The product of the given number and the sum of its digits is equal to 144.
To find:
The two-digit number.
Solution:
Let the ten's digit be x and the unit's digit be x + 2.
The given number can be expressed as 10x + (x + 2).
The sum of the digits can be expressed as x + (x + 2) = 2x + 2.
According to the given condition, the product of the number and the sum of its digits is 144:
(10x + (x + 2))(2x + 2) = 144
Simplifying the equation:
(10x + x + 2)(2x + 2) = 144
(11x + 2)(2x + 2) = 144
Expanding the equation:
22x^2 + 26x + 4 = 144
Rearranging the equation:
22x^2 + 26x - 140 = 0
Dividing the equation by 2:
11x^2 + 13x - 70 = 0
Factoring the quadratic equation:
(11x - 10)(x + 7) = 0
Setting each factor equal to zero and solving for x:
11x - 10 = 0 or x + 7 = 0
11x = 10 or x = -7
x = 10/11 or x = -7
Since the number is a two-digit number, x cannot be a fraction or negative.
Therefore, x = 10/11 is not a valid solution.
Hence, x = -7 is not a valid solution.
Therefore, there is no solution to this equation.
Thus, the given information is inconsistent, and we cannot determine the two-digit number.
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In a two-digit number, if it is known that its unit\'s digit exceeds its ten\'s digit by 2 and that the product of the given number and the sum of its digits is equal to 144,then the number isa) 46 b) 42 c) 26 d) 24 Correct answer is option 'D'. Can you explain this answer?
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In a two-digit number, if it is known that its unit\'s digit exceeds its ten\'s digit by 2 and that the product of the given number and the sum of its digits is equal to 144,then the number isa) 46 b) 42 c) 26 d) 24 Correct answer is option 'D'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about In a two-digit number, if it is known that its unit\'s digit exceeds its ten\'s digit by 2 and that the product of the given number and the sum of its digits is equal to 144,then the number isa) 46 b) 42 c) 26 d) 24 Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a two-digit number, if it is known that its unit\'s digit exceeds its ten\'s digit by 2 and that the product of the given number and the sum of its digits is equal to 144,then the number isa) 46 b) 42 c) 26 d) 24 Correct answer is option 'D'. Can you explain this answer?.
In a two-digit number, if it is known that its unit\'s digit exceeds its ten\'s digit by 2 and that the product of the given number and the sum of its digits is equal to 144,then the number isa) 46 b) 42 c) 26 d) 24 Correct answer is option 'D'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about In a two-digit number, if it is known that its unit\'s digit exceeds its ten\'s digit by 2 and that the product of the given number and the sum of its digits is equal to 144,then the number isa) 46 b) 42 c) 26 d) 24 Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a two-digit number, if it is known that its unit\'s digit exceeds its ten\'s digit by 2 and that the product of the given number and the sum of its digits is equal to 144,then the number isa) 46 b) 42 c) 26 d) 24 Correct answer is option 'D'. Can you explain this answer?.
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In a two-digit number, if it is known that its unit\'s digit exceeds its ten\'s digit by 2 and that the product of the given number and the sum of its digits is equal to 144,then the number isa) 46 b) 42 c) 26 d) 24 Correct answer is option 'D'. Can you explain this answer?, a detailed solution for In a two-digit number, if it is known that its unit\'s digit exceeds its ten\'s digit by 2 and that the product of the given number and the sum of its digits is equal to 144,then the number isa) 46 b) 42 c) 26 d) 24 Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of In a two-digit number, if it is known that its unit\'s digit exceeds its ten\'s digit by 2 and that the product of the given number and the sum of its digits is equal to 144,then the number isa) 46 b) 42 c) 26 d) 24 Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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