# In a class test, the sum of the marks obtained by P in mathematics and science is 28.

Question:

In a class test, the sum of the marks obtained by P in mathematics and science is 28. Had he got 3 more marks in mathematics and 4 marks less in science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained him in the two subjects separately.

Solution:

Let the marks obtained by P in mathematics and science be x and (28 − x), respectively.

According to the given condition,

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

$\Rightarrow(x+3)(24-x)=180$

$\Rightarrow-x^{2}+21 x+72=180$

$\Rightarrow x^{2}-21 x+108=0$

$\Rightarrow x^{2}-12 x-9 x+108=0$

$\Rightarrow x(x-12)-9(x-12)=0$

$\Rightarrow(x-12)(x-9)=0$

$\Rightarrow x-12=0$ or $x-9=0$

$\Rightarrow x=12$ or $x=9$

When x = 12,
28 − = 28 − 12 = 16

When x = 9,
28 − = 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.