Question

the sum of the digits of a 2- digit number is 11. the number obtained by interchanging the digits exceeds the original number by 27. find the number.

Answer 1

Let digit at ones place =x
Digit at tens place=11-x
On interchanging =10(11-x)+x
=110-10x+x
=110-9x
The digit at ones place =11-x
The digit at tens place =x
On interchanging =10×x+11-x
=10x+11-x
=9x+11
A.T.Q
110-9x =27+9x+11
110-38=9x+9x
82=18x
x=82/18
x=4
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