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.

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

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 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.

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  .

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).