Question

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.

Answer 1

Let the marks obtained in mathematics be x then marks in science be 28-x
from given condition,
$(x+3)(28-x-4)=180$
$\Rightarrow (x+3)(24-x)=180$
⇒$24x-x^2+72-3x=180$
⇒$21x-x^2-180+72=0$
⇒$x^2-21x+108=0$
⇒$x^2-12x-9x+108=0$
$\Rightarrow x(x-12)-9(x-12)=0$
$\Rightarrow (x-9)(x-12)=0$
$\therefore x=9,12$
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