Question

The sum of the digit in a two digits’ number is $ 9 $ .The number obtained by interchanging the digit exceeds the original number by $ 27. $ find the two digit number.

Answer 1

Hint: An equation is said to be linear equation in two variables if it is written in the form of $ ax + by + c = 0, $ where $ a,b,c $ are real numbers and the coefficients of $ x $ and $ y, $ i.e. $ a $ and $ b $ respectively, are not equal to zero.

Complete step-by-step answer:
Let the two digit number be $ 10x + y $
Given that the sum of the digit is $ 9 $
 $ x + y = 9 $ . . . . (1)
Given that the number obtained by interchanging the digits exceeds the given number by $ 27 $
 $ 10y + x = 10x + y + 27 $
 $ 9x - 9y = 27 $
 $ x - y = - 3 $
On taking $ 9 $ as common $ x - y = - 3 $ ….(2)
Adding equation (1) and (2) substitution
 $ \Rightarrow 2x = 6 $
 $ \Rightarrow x = 3 $
 $ \Rightarrow 3 + y = 9 $
 $ \Rightarrow y = 6 $
The number is $ 10x + y $ is $ 36. $
So, the correct answer is “36”.

Note: To verify linear equations in two variables are correct we add given values of $ x $ and $ y $ in any given equation. Therefore, adding $ y = 6 $ and $ x = 3 $ in equation $ 10x + y $ we get $ LHS = RHS $ . The digit sum of a number, say $ 152 $ , is just the sum of the digits $ 1 + 5 + 2 = 8 $ .