# A two-digit number is such that the product of the digits is 12. When 36 is added to the number the digits interchange their places. Determine the number.

Let the ones digit be ‘a’ and tens digit be ‘b’.

Given, two-digit number is such that the product of its digits is 12.

ab = 12 --- (1)

Also, when 36 is added to the number, the digits interchange their places

10b + a + 36 = 10a + b

9a – 9b = 36

a – b = 4

a = 4 + b

Substituting in 1

b × (4 + b) = 12

b2 + 4b – 12 = 0

b2 + 6b – 2b – 12 = 0

b(b + 6) – 2(b + 6) = 0

(b – 2)(b + 4) = 0

b = 2

Thus, a = 6

Number is 26

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Bonus Questions on Solutions of Quadratic Equations31 mins
Smart Revision | Quadratic Equations53 mins
Quiz | Knowing the Nature of Roots44 mins
Take a Dip Into Quadratic graphs32 mins
Foundation | Practice Important Questions for Foundation54 mins
Learn to Find Nature of Roots25 mins
Smart Revision | Learn to Find the Nature of Roots34 mins
Nature of Roots of Quadratic Equations51 mins
Getting Familiar with Nature of Roots of Quadratic Equations51 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
view all courses