# The sum of the digits of a two number is 12. the f 54 is subtracted from the number, the digits get reversed. find the number

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A/q,

x+y =12

and, (10x +y) -54 = (10y +x)

⇒9x -9y = 54

⇒x-y =6

⇒x =(6 +y), putting this value in first equation,

(6 +y) +y =12

⇒2y =6

⇒y =3

so, x= 6+3 =9

Let the digits of the number be x and y

the number = 10x+y

Given x+y = 12 --------------------(1)

Also given 10x+y -54 = 10y+x

⇒10x + y - 10y - x = 54

⇒9x - 9y - 54 = 0

⇒9( x - y - 6 = 0)

⇒x - y -6 = 0/9

⇒ x - y = 6 --------------------(2)

Adding (1) from (2)

x + y = 12

x - y = 6

⇒2x - 0 = 18

⇒ x = 18/2

∴x = 9

Substituting x = 9 in (1)

⇒ x+y =12

⇒9+y = 12

⇒y = 12-9

∴ y = 3

Therefore the number is 10x + y

= 10(9) + 3

= 90 + 3

= 93

∴The number is 93

the number = 10x+y

Given x+y = 12 --------------------(1)

Also given 10x+y -54 = 10y+x

⇒10x + y - 10y - x = 54

⇒9x - 9y - 54 = 0

⇒9( x - y - 6 = 0)

⇒x - y -6 = 0/9

⇒ x - y = 6 --------------------(2)

Adding (1) from (2)

x + y = 12

x - y = 6

⇒2x - 0 = 18

⇒ x = 18/2

∴x = 9

Substituting x = 9 in (1)

⇒ x+y =12

⇒9+y = 12

⇒y = 12-9

∴ y = 3

Therefore the number is 10x + y

= 10(9) + 3

= 90 + 3

= 93

∴The number is 93