# 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.

Let the units digit be ‘Y’, so the tens digit will be X.

the number is 10X + Y

X . Y =14 –––––– (i)

On simplifying further,

9X – 9Y + 45 = 0

X – Y + 5 = 0

Putting the value of from equation –––––– (i)

14 – Y2 + 5Y = 0

Y2 – 5Y – 14 = 0

On applying Sreedhracharya formula

Y = – 2 or 7

Y = 7 (Only Positive values)

X = 2

The number is 27 {2 (10) + 7}.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
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 EquationsFREE Class
Getting Familiar with Nature of Roots of Quadratic Equations51 mins
Quadratic Equation: Previous Year NTSE Questions32 mins
Champ Quiz | Quadratic Equation33 mins
Champ Quiz | Quadratic Equation48 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