Q. 254.8( 8 Votes )

A two – digit number is such that the product of its digits is 14. If 45 is added to the number, the digits interchange their places. Find the number.

Answer :

Let the digits at units and tens place be x and y respectively

xy = 14


– – – – (1)


According to the question


(10y + x) + 45 = 10x + y


9y – 9x = – 45


y – x = – 5 – – – – – (2)


From (1) and (2) we get




14 – x2 = – 5x


x2 – 5x – 14 = 0


Using the splitting middle term – the middle term of the general equation is divided in two such values that:


Product = a.c


For the given equation a = 1 b = – 5 c = – 14


= 1. – 14 = – 14


And either of their sum or difference = b


= – 5


Thus the two terms are – 7 and 2


Difference = – 7 + 2 = – 5


Product = – 7.2 = – 14


x2 – 5x – 14 = 0


x2 – 7x + 2x – 14 = 0


x(x – 7) + 2(x – 7) = 0


(x + 2)(x – 7) = 0


x = 7 or x = – 2


x = 7 (neglecting the negative part)


Putting x = 7 in equation (1) we get


y = 2


Required number = 10.2 + 7 = 27


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Get To Know About Quadratic Formula42 mins
Quiz | Knowing the Nature of Roots44 mins
Take a Dip Into Quadratic graphs32 mins
Foundation | Practice Important Questions for Foundation54 mins
Nature of Roots of Quadratic Equations51 mins
Getting Familiar with Nature of Roots of Quadratic Equations51 mins
Quadratic Equation: Previous Year NTSE Questions32 mins
Champ Quiz | Quadratic Equation33 mins
Understand The Concept of Quadratic Equation45 mins
Balance the Chemical Equations49 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