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.

Question

chapter playing with number class 8th

Answer 1

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