Question

Sum of the digits of a two- digit number
is 9. When ne interchange the digits
It is found that the resulting new
number is greater than the orignal
number by 27. What is the two
digit number 2 2​

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,

$\longrightarrow \sf x+y = 9 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ - Eq(i)$

According to the second condition,

$\longrightarrow \sf 10x+y+27 = 10y+x \\\\\longrightarrow 10x-x+y-10y= -27 \\\\\longrightarrow 9x-9y = -27\\\\\longrightarrow x- y = - 3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ - Eq(ii)$

Add eq(i) and eq(ii),

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

Substitute the value of x in eq(i),

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

Two digit number = 36