The sum of digits of a 2-digit number is 11.If the number obtained by reversing the digit is 9 less than the original number,find the number.
let the two digits be A and B.
Let the two-digit number be N.
Then N = AB
i.e. N = 10*A + B
Let the second number be M
Then M = BA
i.e. M = 10*B + A
But M = N - 9
i.e. 10B + A = 10A + B - 9
9B - 9A + 9 = 0
or, A - B = 1
But we also have A + B = 11 (sum of digits = 11)
so,
A - B = 1
A + B = 11
2A = 12, A = 6, B = 5
The number N is N = 65