Question:
In a class test, the sum of the marks obtained by P in Mathematics and science 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 his marks in two subjects.
Solution:
Let marks obtained by $P$ in mathematics be $x$, then in science $=(28-x)$
It is given that,
$(x+3) \times(28-x-4)=180$
$(x+3) \times(24-x)=180$
$24 x-x^{2}+72-3 x=180$
$-x^{2}+21 x+72-180=0$
$-\left(x^{2}-21 x+108\right)=0$
$x^{2}-21 x+108=0$
$x^{2}-12 x-9 x+108=0$
$x(x-12)-9(x-12)=0$
$(x-12)(x-9)=0$
Therefore, when $x=12$ then
$(28-x)=(28-12)$
$=16$
Hence, marks in mathematics $x=12$ and marks in science $=16$.
Or, when $x=9$ then
$(28-x)=(28-9)$
$=19$
Hence, marks in mathematics $x=9$ and marks in science $=19$.