The sum of the digits of a two digit number is 13 the number obtained by interchanging the digits of the given number exceeds that number by 27 find the number
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The sum of the digits of a two digit number is 13 the number obtained by interchanging the digits of the given number exceeds that number by 27 find the number
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And unit place digit be b
According to first condition,
a + b = 13 -----(1)
According to second condition,
(10b+ a) - (10a + b) = 27
=> 10b + a - 10a - b = 27
=> 9b - 9a = 27
=> b - a = 3 ------(2)
On adding equation 1 and 2, we get
2b = 16
=> b = 8
Now,
On substituting the value of b in equation 1, we get
a + 8 = 13
=> a = 5
Number = 58
Let the digit at unit's place be y.
Therefore the original number is 10x + y -------- (*)
On interchanging the original number, we get 10y + x.
Given that sum of digits of a two digit number is 13.
= > x + y = 13. ------ (1)
Given that the number obtained by interchanging the digits of the given number exceeds that number by 27.
= > 10y + x = 10x + y + 27
= > 9y - 9x = 27
= > y - x = 3 ------ (2)
On solving (1) & (2), we get
= > x + y = 13
= > -x + y = 3
---------------
2y = 16
y = 8.
Substitute y = 8 in (1), we get
= > x + y = 13
= > x + 8 = 13
= > x = 13 - 8
= > x = 5.
Substitute x = 5 and y = 8 in (*), we get
= > The original number = 10x + y
= 10(5) + 8
= 50 + 8
= 58.
Therefore the number is 58.
Hope this helps!