when the digits of two digits number are reversed the number increase by 27 the sum of such two digit number is
Answers
Answer:
Sum of two digit is odd number, such that sum is greater than equal to 5 and less than equal to 15
Step-by-step explanation:
Let the unit digit of two digit number be x
Let the ten's digit of two digit number be y
Thus, the number = 10y + x
Reverse Number = 10x + y
Also, Given that when digits are reversed, the number increase by 27
Thus, we get
10x + y = 10y + x + 27
(10x - x) + (y - 10y) = 27
9x - 9y = 27
x - y = 3
x = y + 3
We need to find , two digits such that digit at unit place is 3 more than digit at ten's place
possible values of x and y are
x = 3, y = 0
x = 4, y = 1
x = 5, y = 2
x = 6, y = 3
x = 7, y = 4
x = 8, y = 5
x = 9, y = 6
Now, checking to find which combination is the possible answer
When x = 3, y = 0
Digit = 03 - Its is not a two digit number, hence this is not possible
When x = 4, y = 1
Digit = 14
Reverse = 41
Now,14 + 27 = 41
Sum = 1 + 4 = 5
When x = 5, y = 2
Digit = 25
Reverse = 52
Now,25 + 27 = 52
Sum = 5 + 2 = 7
When x = 6, y = 3
Digit = 36
Reverse = 63
Now,36 + 27 = 63
Sum = 6 + 3 = 9
When x = 7, y = 4
Digit = 47
Reverse = 74
Now,47 + 27 = 74
Sum = 7 + 4 = 11
When x = 8, y = 5
Digit = 58
Reverse = 85
Now, 58 + 27 = 85
Sum = 8 + 5 = 13
When x = 9, y = 6
Digit = 69
Reverse = 96
Now,69 + 27 = 96
Sum = 6 + 9 = 15