Question

2
Sum of two digits of a 2-digit number is 12. If the digits are reversed, the new
number so formed increases by 36. Find the original number.
SET​

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,

$\longrightarrow \sf 10x+y+36= 10y+x\\\\\longrightarrow 10x-x+y-10y= -36 \\\\\longrightarrow 9x-9y = - 36\\\\\longrightarrow x- y = -4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .............(2)$

Add equation (1) and equation (2),

$\longrightarrow\sf 2x = 8 \\\\\longrightarrow\bf x = 4$

Substitute the value of x in eq (1),

$\longrightarrow \sf 4+y = 12 \\\\\longrightarrow \bf y = 8$

Two digit number = 48