This is the basic and conceptual question from linear equations in two variables in which we have to find the number is their sum of digits is 15 and the digit formed by interchanging their digits exceed the number by 9.
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 3E, question no 13
Let the units digit be x and tens digit be y.
Then, x+y=15 ……….(i)
Given number: 10y+x
Interchanged digits: 10x+y
A.t.Q:-
⇒(10x+y)−(10y+x)=9
⇒10x+y−10y−x=9
⇒9x−9y=9
⇒x−y=1 ………(ii)
Solving (i) and (ii)
x=8, y=7
∴ Two digit number=78.