Question

A number consists of two digits. If the number formed by interchanging the digits is added to the original number, the resulting number (i.e., the sum) must be divisible by

Answer 1

Let the ten's digit be x and unit's digit be y.
Then, number = 10x + y.
Number obtained by interchanging the digits = 10y + x.

∴ (10x + y) + (10y + x) = 11(x + y)


which is divisible by 11.

Answer 2

Given :

The number consists of two digits

To find :

The number which divides the given number

Solution :

• The number is a two digit number.lets tens place digit be a and units place digit be b

• The number be 10a + b

• The number formed by interchanging the digits = 10b + a

• Sum of numbers = 10a+b+10b+a

                            =11a + 11b   =11(a+b)

• The given number is divisible by 11