Question

Show that a two digit number added to 8 times the number formed by reversing the digits is
always divisible by 9.
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Answer 1

Step-by-step explanation:

show that a two digit number added to 8 times the number formed by reversing the digits always divisible by 9

Let the digit on ten’s place be x and the digit on one’s place be y

We know that for example 16 can be written as 1 x 10 + 6 x 1

So the number can be taken as 10 x + y

According to the question we get

10 x + y + 8(10 y + x) (also by reversing)

10 x + y + 80 y + 8 x

18 x + 81 y is the equation.

Taking an example as x = 1 and y = 5 we get

18(1) + 81(5)

18 + 405 = 423 (423 / 9 = 47 divisible by 9)

Let x = 2 and y = 4

36 + 324 = 360 (divisible by 9)