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When a two digit number is multiplied by the sum of its digits, the product is 424. When its digits are interchanged, the number obtained is multiplied by the sum of the digits, then the product is 280. The sum of the digits of that number is: (1) 6 (2) 9 (3) 8 (4) 7?
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When a two digit number is multiplied by the sum of its digits, the pr...
Solution:
Let the two-digit number be 10a + b, where a and b are the digits.
First condition:
10a + b * (a + b) = 424
=> 10a^2 + 11ab + b^2 = 424
Second condition:
10b + a * (a + b) = 280
=> 10b^2 + 11ab + a^2 = 280
From the above two equations, we get:
a^2 - b^2 = 144
=> (a + b)(a - b) = 144
Since the number is a two-digit number, a and b are between 1 and 9.
Factors of 144:
1 * 144, 2 * 72, 3 * 48, 4 * 36, 6 * 24, 8 * 18, 9 * 16, 12 * 12
Only pair that satisfies the condition is:
a + b = 12
a - b = 12
=> a = 6, b = 6
Sum of the digits of the number obtained by interchanging the digits:
= 6 + 6
= 12
Therefore, the sum of the digits of the number is 12.
Let the two-digit number be 10a + b, where a and b are the digits.
First condition:
10a + b * (a + b) = 424
=> 10a^2 + 11ab + b^2 = 424
Second condition:
10b + a * (a + b) = 280
=> 10b^2 + 11ab + a^2 = 280
From the above two equations, we get:
a^2 - b^2 = 144
=> (a + b)(a - b) = 144
Since the number is a two-digit number, a and b are between 1 and 9.
Factors of 144:
1 * 144, 2 * 72, 3 * 48, 4 * 36, 6 * 24, 8 * 18, 9 * 16, 12 * 12
Only pair that satisfies the condition is:
a + b = 12
a - b = 12
=> a = 6, b = 6
Sum of the digits of the number obtained by interchanging the digits:
= 6 + 6
= 12
Therefore, the sum of the digits of the number is 12.
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When a two digit number is multiplied by the sum of its digits, the product is 424. When its digits are interchanged, the number obtained is multiplied by the sum of the digits, then the product is 280. The sum of the digits of that number is: (1) 6 (2) 9 (3) 8 (4) 7?
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When a two digit number is multiplied by the sum of its digits, the product is 424. When its digits are interchanged, the number obtained is multiplied by the sum of the digits, then the product is 280. The sum of the digits of that number is: (1) 6 (2) 9 (3) 8 (4) 7? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about When a two digit number is multiplied by the sum of its digits, the product is 424. When its digits are interchanged, the number obtained is multiplied by the sum of the digits, then the product is 280. The sum of the digits of that number is: (1) 6 (2) 9 (3) 8 (4) 7? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When a two digit number is multiplied by the sum of its digits, the product is 424. When its digits are interchanged, the number obtained is multiplied by the sum of the digits, then the product is 280. The sum of the digits of that number is: (1) 6 (2) 9 (3) 8 (4) 7?.
When a two digit number is multiplied by the sum of its digits, the product is 424. When its digits are interchanged, the number obtained is multiplied by the sum of the digits, then the product is 280. The sum of the digits of that number is: (1) 6 (2) 9 (3) 8 (4) 7? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about When a two digit number is multiplied by the sum of its digits, the product is 424. When its digits are interchanged, the number obtained is multiplied by the sum of the digits, then the product is 280. The sum of the digits of that number is: (1) 6 (2) 9 (3) 8 (4) 7? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When a two digit number is multiplied by the sum of its digits, the product is 424. When its digits are interchanged, the number obtained is multiplied by the sum of the digits, then the product is 280. The sum of the digits of that number is: (1) 6 (2) 9 (3) 8 (4) 7?.
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