Question

The sums of the digits of a two digits numbers is 12 if the new number formed by revering that digits is greter then the original number by 54,fined the original number

Answer 1

SOLUTION :-

Let,

Digit in ten's place = x

Digit in one's place = y

Two digit number = 10x + y

According to the first condition,

$\longrightarrow\sf x + y = 12 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .................(1)$

According to the second condition,

$\longrightarrow\sf 10x+y+54 = 10y+x \\\\\longrightarrow\sf 10x-x+y-10y = -54 \\\\\longrightarrow 9x-9y = -54 \\\\\longrightarrow x-y = -6 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .................(2)$

Add equation (1) and equation (2),

$\longrightarrow\sf 2x= 6\\\\\longrightarrow \bf x= 3$

Substitute the value of x in equation (1),

$\longrightarrow\sf 3 +y = 12\\\\\longrightarrow\bf y = 9$

Digit in ten's place = 3

Digit in one's place = 9

Two digit number = 39