Question

the sum of digits of 2 digit number is a 9. also 9 times the number is twice the number obtained by reversing the digit of the number. find the number?​

Answer 1

ANSWER:-

Given:

The sum of digits of 2 digit number is 9. Also 9 times the number is twice the number obtained by reversing the digit of the number.

To find:

Find the number.

Solution:

Let x be the digit at the units place &

Let y be the digit at the tens place.

According to the question:

x+y= 9...........(1)

&

The original number is x +10y

On reversing, we get the new number is

=) y+ 10x

Therefore,

9(x+10y) = 2(y+10x)

=) 9x + 90y = 2y+ 20x

=) 9x -20x= 2y -90y

=) -11x = -88y

=) x= 8y.........(2)

Now,

Putting the value of x in equation (1), we get;

=) 8y + y =9

=) 9y= 9

=) y= 9/9

=) y=1

Eliminate y in equation (2), we get;

=) x= 8(1)

=) x= 8

Hence,

The number is 18.

Hope it helps ☺️