Question

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

Answer 1

Let the marks of mathematics and science be x and 28-x respectively.
Given :-
Mathematics: x+3
Science: 28-x-4= 24-x
.: Their product=( x+3)(24-x)
=24x-x^2+72-3x
= 21x-x^2+72
But given product= 180
=> 21x-x^2+72=180
=>x^2-21x-72+180=0
=>x^2-21x+108=0
=>x^2-12x-9x+108=0
=>x(x-12)-9(x-12)=0
=>(x-9)(x-12)= 0
.: x= 9 or 12
When x= 9
Marks are 9 and 19
When x= 12
Marks are 12 and 16.

Answer 2

Let the marks obtained in science be x
Marks obtained in maths = 28-x

If 3 more in maths and 4 less in science, then product=180
=> (28-x+3)(x-4)=180
=> (31-x)(x-4)=180
=> 31x-x2+4x-124=180
=> x2-35x+304=0
=x2-19x-16x+304=0
=> x(x-19)-16(x-19)=0
=> (x-16)(x-19)=0
=> x=16,19
=> Science mark=16,12
=> Maths mark=9,19