Question

The difference between a two-digit number and the number formed by reversing it's digits,and the sum of these two numbers are always exactly divisible by
A)5and 7respectively
B)9 and 11 respectively
C)11 and 9 respectively
D)7and 5 respectively

Answer 1

Dear Student,
Let the digit in the units place be y and the digit in the tens place be x.
Then the number would be 10x+y and on reversing the digits, the number would be 10y+x
The difference of the numbers would be (10x+y)-(10y+x)=9x-9y=9(x-y) ,i.e divisible by 9
The sum of the two numbers would be 10x+y+10y+x= 11x+11y=11(x+y),i.e divisible by 11
Thus the required digits are 9 and 11 respectively(Option B)
Regards.