Question

The sum of the of 2 digit number id 12 . If the new number formed by reversing the digits is greater than the original number by 18, find the oirignal number. check your answer.

Answer 1

Correct Question :-

The sum of digits of a two digit number is 12. If the new number formed by reversing the digits is greater that the original number by 18. find the original number.

Solution :-

Let :-

Digit in ten's place = x

Digit in one's place = y

According to the first condition :-

$\longrightarrow \sf x+y = 12 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .....................(1)$

According to the second condition :-

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

Equation (2) + Equation (1) :-

$\longrightarrow \sf 2x = 10 \\\\\longrightarrow \bf x = 5$

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

$\longrightarrow \sf 5+y = 1 2 \\\\\longrightarrow \bf y = 7$

Original number = 57