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The sum of the digits of a two digit number is 8. When 18 is added to the number, the digits are reversed. Find the number?
Correct answer is '35'. Can you explain this answer?
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The sum of the digits of a two digit number is 8. When 18 is added to ...
Let the two digits be x and y (and the original no. = 10x +y)
since, the sum of the digits is 8 => x+y = 8 (eq. 1);
after adding 18 to the no. => 10x + y + 18 = 10y + x (digits getting reversed)
=> 18 = -9x + 9y => 2 = -x + y (eq. 2)
compare eq. 1 and 2 : x will be crossed off and 2y = 10; => y = 5
since y = 5 and x + y = 8; x = 8 - 5 = 3.
Therefore, the original no. = 10x + y = 10*3 + 5 = 35.
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The sum of the digits of a two digit number is 8. When 18 is added to ...
Given Information:
The sum of the digits of a two-digit number is 8.
When 18 is added to the number, the digits are reversed.
Solution:
Let's assume the two-digit number is represented by 10a + b, where a and b are the digits.
- The sum of the digits: a + b = 8
- The number after adding 18 and reversing the digits: 10b + a + 18
According to the given information:
10a + b + 18 = 10b + a
Substitute the values of a and b:
10(8 - b) + b + 18 = 10b + 8
80 - 10b + b + 18 = 10b + 8
98 - 9b = 10b + 8
90 = 19b
b = 5
Substitute the value of b back into the equation:
a = 8 - b
a = 8 - 5
a = 3
Therefore, the two-digit number is 10a + b = 10(3) + 5 = 30 + 5 = 35.
Hence, the number is 35.
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The sum of the digits of a two digit number is 8. When 18 is added to the number, the digits are reversed. Find the number?Correct answer is '35'. Can you explain this answer?
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