# In a class test, the sum of the marks obtained by P in mathematics and science is 28. Had he got 3 more marks in mathematics and 4 marks less in science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained by him in the two subjects separately.

Let the marks obtained by P in mathematics and science be x and (28 – x) respectively

According to the given condition,

(x + 3)(28 – x – 4) = 180

(x + 3)(24 – x) = 180

– x2 + 21x + 72 = 180

x2 – 21x + 108 = 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 = – 21 c = 108

= 1.108 = 108

And either of their sum or difference = b

= – 21

Thus the two terms are – 12 and – 9

Difference = – 12 – 9 = – 21

Product = – 12. – 9 = 108

x2 – 12x – 9x + 108 = 0

x (x – 12) – 9 (x – 12) = 0

(x – 12) (x – 9) = 0

(x – 12) = 0 or (x – 9) = 0

x = 12, x = 9

When x = 12,

28 – x = 28 – 12 = 16

When x = 9,

28 – x = 28 – 9 = 19

Hence he obtained 12 marks in mathematics and 16 science or

He obtained 9 marks in mathematics and 19 science.

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  Champ Quiz | Quadratic Equation33 mins  Quadratic Equation: Previous Year NTSE Questions32 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 