Question

5.
The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits is
greater than the original number by 18, find the original number.​

Answer 1

Let unit place digit = x

Ten's place digit = 12 - x

/* Since , sum of the digits = 12 (given ) */

Original number = 10(12-x) + x

= 120 - 10x + x

= 120 - 9x ----(1)

If reversing the digits the new number so formed is 10x + 12 - x

= 9x+ 12 ----(2)

/*According to the problem given */

9x + 12 - ( 120 - 9x ) = 18

=> 9x + 12 - 120 + 9x = 18

=> 18x = 18 - 12 + 120

=> 18x = 6 + 120

=> 18x = 126

=> x = 7

Therefore.,

Original number = 120 - 9x [ From (1) ]

= 120 - 9 × 7

= 120 - 63

= 57

•••♪

Answer 2

Let the no. at ones digit be x

and the no. at tens digit be y

so the sum of the digits= x+y=12 ___ 1

Original number=10× y+1× x

=10y+x

If the digits are reversed,

New number=10×x+1×y

=10x+y

according to question,

10x+y = 18 + 10y+ x

9x = 18 + 9yv

9x-9y=18

9(x-y)=18

x-y=18/9=2 ___ 2

adding 1 and 2

we get,

2x=14

x=7

and y=5

ORIGINAL NUMBER=10×5 + 7

=57

HOPE IT HELPS.......

PLZ MARK AS BRAINLIEST