In a class test, the sum of 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 in two subjects separately.

P    got      (X) mark in math ,    (28 – X)  mark in science ,  So  (X+3)((28 – X – 4)  =180  .OR  (X +3)( 24 – X) =180 .  OR  21X – X^2 +72 = 180, OR  180 – 72 – 21X + X^2  = 0  OR   108 – 21X + X^2 = 0 .     OR  (X -12)(X – 9)  =0  .

   P   got mark(  MATH  =9 ,science =19)  OR (MATH= 12,Science = 16) ANSWER  .

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.

Let marks of maths be x

And marks of science be y

According to question

X + Y =28.....(1)

(X+3)(Y-4)=180......(2)

(X+3)(28-X-4)=180.....(putting value of y from equation 1)

(X+3)(24-x)=180

Solving the equation we will get

X=12,9

Using equation 1

Y=16,19respectively

Let the marks of mathematics be x 

Then marks of science be 28-x ,

now according to question 

(x+3), 

(28-x-4)

The product of new marks will be 180

So, 

(x+3) (28-x-4)=180,

24x-x^2+72-3x=180

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)=0 than x=9

(x-12)=0than x=12

If 9 marks got in math than 19 marks got in science

If 12 marks got in math than 16 marks got in science

m >>>> Marks in maths.

s >>>>> Marks in science

m+s= 28 >>>>> m=28-s

(m+3)(s-4)=180

(31-s)(s-4)=180

-s^2+35s-124=180

s^2-35s+304=0

(s-16)(s-19)=0

s=16, 19

When s=16, m=12

When s=19, m=9

Hence the possible marks in subject maths and science are respectively (9, 19); (12, 16).