Answer :

Let the two-digit number be xy(i.e. 10x + y).


After reversing the digits of the number xy, the new number becomes yx (i.e. 10y + x).


According to question –


xy = 35…..(1)


And,


(10x + y) + 18 = (10y + x)


9x – 9y = – 18


x – y = – 2…..(2)


From equation(2), we get –


x = y – 2…..(3)


Substitute the value of x in equation(1), we get –


y(y – 2) = 35


y2 – 2y – 35 = 0


y2 – 7y + 5y – 35 = 0


y(y – 7) + 5(y – 7) = 0


(y – 7)(y + 5) = 0


y = 7 [ y = – 5 is invalid because digit of a number can't be – ve.]


Substituting the value of y in equation (3), we get –


x = 5


Thus, the required number is 57.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Trigonometric Identities-IITrigonometric Identities-IITrigonometric Identities-II43 mins
Check What you know- Quiz Part IICheck What you know- Quiz Part IICheck What you know- Quiz Part II43 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Solve each of theRS Aggarwal - Mathematics

If 2x – 3y = 7 anRD Sharma - Mathematics

Solve the followiRD Sharma - Mathematics