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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.


Solution

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.

Mathematics

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