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. [CBSE 2008]

Answer 1

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

According to the given condition,
$$\begin{gathered} \left(x+3\right)\left(28-x-4\right)=180 \\ \Rightarrow \left(x+3\right)\left(24-x\right)=180 \\ \Rightarrow -x^2+21x+72=180 \\ \Rightarrow x^2-21x+108=0 \end{gathered}$$
$$\begin{gathered} \Rightarrow x^2-12x-9x+108=0 \\ \Rightarrow x\left(x-12\right)-9\left(x-12\right)=0 \\ \Rightarrow \left(x-12\right)\left(x-9\right)=0 \\ \Rightarrow x-12=0\mathrm{or}x-9=0 \end{gathered}$$
$\Rightarrow x=12\mathrm{or}x=9$

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.