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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