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 the two subjects.

Answer 1

Let $P$ has obtained $x$ in mathematics and $y$ in science.

Then by the problem,

$x+y=28$.......(1).

If $P$ would have got $3$ marks more in mathematics, then $P$ would have got $(x+3)$ in mathematics and if $P$ would have got $4$ marks less in science then $P$ would have got $(y-4)$ in science.

Also

$(x+3)(y-4)=180$

or, $(x+3)(24-x)=180$

or, $72+21x-x^2=180$

or, $x^2-21x+108=0$

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

or, $x=12,9\Rightarrow y=16,19$.

There may be two situation.

$P$ obtained $12$ marks in mathematics and $16$ in science.

or,

$P$ obtained $9$ marks in mathematics and $19$ in science.