Question

9. 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

Answer:

Let the marks obtained by P in mathematics and science be $x$ and $(28-x)$.

According to the given condition,

$(x+3)(28-x-4)=180$

⇒ $(x+3)(24-x)=180$

⇒ $-x^{2}+21x+72=180$

⇒ $x^{2} -21x+180$

⇒ $x^{2} -12x+9x+108=0$

⇒ $x(x-12)-9(x-12)=0$

⇒ $(x-12) (x-9)=0$

⇒ $x-12=0$ or $x-9=0$

⇒$x=12$ or $x=9$

when $x=12$,

$28-x=28-12=16$

when $x=9$,

$28-x=28-9=19$

Hence, he obtained 12 marks in mathematics and 16 marks in science or 9 marks in mathematics and 19 marks in science.