Question

The sum of the digits of a two digit number is 12. lf 54 is subtracted from the number, the digits get reversed. Find the number.

Answer 1

Let the digit in the tens place be "x" and in one's place be "y".

Then the number= 10 x + y.

Given, sum of the digits = 12.

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

ATP,

10x + y - 54 = 10y + x

10x - x -54 = 10y - y.

9x - 54 = 9y

9x - 9y = 54

9 ( x-y ) = 54

x-y = 54/9

x-y = 6 ----------------------- ( 2 )


Solving (1) and (2).

x+y + x-y = 12 + 6

2x = 18.

x = 18/2

x = 9.

Substituting x = 9 in (1), we get

x + y = 12

9 + y = 12

y = 12 - 9

y = 3.

The number = 10x + y = 10(9)+3 = 90+3 = 93.

So, the number is 93.

:)

Answer 2

Let tens place digit =x
Unit place digit=12-x
The number =10x+(12-x)
=9x+12---(1)
If 54 is subtracted feom the num= reverse the number
9x+12-54=10(12-x)+x
9x-42=120-10x+x
9x+10x-x=120+42
18x=162
x=9
Therefore Required number =9x+12
=9*9+12
=81+12
=93