Question

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 54,
find the original number.​

Answer 1

Answer:

let the no. at ones digit be x

no. at tens digit=12-x

original no.=10(12-x)+x

120-10x+x

120-9x

no. formed by reversing the digits=10x+12-x

9x+12=120-9x+54

9x+12=174-9x

9x+9x=174-12

18x=162

x=162/18=9

original no.=120-9x

120-9×9

120-81

39

hope it helps.......

Answer 2

let,

ones digit =x

tens digit=y

the no. be =10y+x

a/q

x+y=12 ............1

10y+x-54=10x+y

10y-y+x-10x=54

9y-9x=54

9[y-x]=54

y-x=54/9

-x+y=6...........2

x+y=12.......1

2y=18

y=18/2

y=9

put the value of y in eq.1

x+y=12

x+9=12

x=12-9

x=3

the no. be = 10y +x

= 10×9+3

=90+3=93.

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