Question

the sum of the digits of a two digit number is 9 and the difference between the number and that formed by reversing the digits is 27. find the 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,

$\longrightarrow\sf x+y= 9 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...................(1)$

According to the second condition,

$\longrightarrow\sf (10x+y)-(10y+x) = 27 \\\\\longrightarrow 10x+y-10y-x = 27 \\\\\longrightarrow 9x-9y = 27 \\\\\longrightarrow x-y = 3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .......................(2)$

Eq (2) + Eq (1),

$\longrightarrow\sf 2x = 12 \\\\\longrightarrow\bf x = 6$

Substitute the value of x in eq (1),

$\longrightarrow\sf 6 + y = 9 \\\\\longrightarrow \bf y = 3$

Two digit number = 63