Question

the sum of the digits of a two digits number is 11 the number got by interchanging the digits is 27 more than the origanal number. what is the number​

Answer 1

SOLUTION :-

Let,

Digit in ten's place = x

Digit on one's place = y

Two digit number = 10x + y

According to the first condition,

$\longrightarrow \sf x+y = 11 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...................(1)$

According to the second condition,

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

Equation (2) + Equation (1),

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

Substitute the value of x in equation (1),

$\longrightarrow \sf 4+y = 11 \\\\\longrightarrow\bf y = 7$

TWO DIGIT NUMBER = 47