Question

Sum of the digit of a two digit number 4 the number got by interchanging the digit is 18 less than the orginal number. What is the number

Answer 1

Solution :-

Let,

Digit in ten's place = x

Digit in one's place = y

Original number = 10x + y

According to the first condition :-

$\longrightarrow \sf x+y = 4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...............(1)$

According to the second condition :-

$\longrightarrow \sf 10x+y-18 = 10y + x \\\\\longrightarrow 10x+y-10y-x = 18 \\\\\longrightarrow 9x-9y = 18 \\\\\longrightarrow x - y= 2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...............(2)$

Add eq (2) and eq (1) :-

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

Substitute the value of x in eq (1) :-

$\longrightarrow \sf 3 + y= 4 \\\\\longrightarrow \bf y = 1$

Original number = 31