Question

in a class test the sum of the marks obtained by p in mathematics and sciene is 28. had he got 3 marks more in mathematics and 4 marks less in science the product of his marks would have been 180. find the marks in the two subjects.

Answer 1

Let the marks obtained in mathematics be x then marks in science be 28-x 
acc,
(x+3)(28-x-4)=180
⇒(x+3)(24-x)=180
⇒24x-x²+72-3x=180
⇒21x-x²-180=0
⇒x²-21x+180=0
⇒x²-12x-9x+108=0
⇒x(x-12)-9(x-12)=0
⇒(x-9)(x-12)=0
∴x=9,12
the marks scored in maths can be 9 or 12
if she got 12 in maths then she got 28-12=16 in science
if she got 9 in maths then she got 28-9=19 in science
hope it helps u

Answer 2

SOLUTION :  

Let the marks obtained by P in  Maths be x.

Then, the marks in science will be 28 - x.

A.T.Q

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

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

24x - x² + 72 - 3x = 180

-x² + 21x  + 72 - 180 = 0

-x² + 21x  + 72 - 108 = 0

x² - 21x + 108 = 0

x² - 12x - 9x + 108 = 0

[By middle term splitting]

x(x - 12) - 9(x - 12) = 0

(x - 12) (x - 9) = 0

(x - 12) = 0 or  (x - 9) = 0

x = 12  or x = 9

Case 1 :  

If the marks in Maths are 12, then marks in science will be = 28 - x = 28 - 12 = 16

Case 2:  

If the marks in Maths are 9, then marks in science will be 28 - 9 = 19

Hence, the marks in Maths are (12,9) and marks in science are (16,19)

HOPE THIS ANSWER WILL HELP YOU.