Question

the sum of the digit of two digit number is 12 if the new number formed by reversing the digit is greater than the original number by 54 find the original number

Answer 1

let the two digit number be xy and given x + y = 12

the new number formed be reversing the digits is yx

given yx is greater than xy by 54

⇒ yx - 54 = xy

yx can be written as 10y + x and xy can be written as 10x + y

substituting the values of yx and xy in the above equation we get

⇒ 10y + x - 54 = 10x + y

⇒ 9y - 9x = 54

⇒ y - x = 6

we know that x + y = 12 we got y - x = 6

⇒ 2y = 18

⇒ y = 9

⇒ x = 3

so the original number is 39

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Assumption

Unit digit be t

Also,

Tens digit be p

So,

Number = 10p + t

So,

Reversed number = 10t + p

Situation,

First,

p + t = 12

t = 12 - p .... (1)

Second,

10t + p = 10p + t + 54

10t - t - 10p + p = 54

9t - 9p = 54

From (1) we have,

9(12 - p) - 9p = 54

108 - 9p - 9p = 54

-18p = 54 - 108

-18p = -54

p = 54/18

p = 3

Substitute the value of p in (1),

t = 12 - p

t = 12 - 3

t = 9

So

Number = 10p + t

= 10(3) + 9

= 39

Therefore,

Required number = 39