Q5. In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.

Let Shefali’s marks in Mathematics = x
Let Shefali’s marks in English = 30 - x
If, she had got 2 marks more in Mathematics, her marks would be = x + 2
If, she had got 3 marks less in English, her marks in English would be = 30 – x - 3 = 27 - x
According to given condition:
$$(x + 2) (27 - x) = 210$$
=>$$27x - x^2 + 54 - 2x = 210$$
=>$$x^2 - 25x + 156 = 0$$
Comparing quadratic equation $$x^2 - 25x + 156 = 0$$ with general form $$ax^2 + bx + c = 0$$,
We get a = 1, b = ?25 and c = 156
Applying Quadratic Formula = $$x = {{-b ± \sqrt{b^2 - 4ac}} \over {2a}}$$
=>$$x = {{25 ± \sqrt{(25)^2 - 4(1)(156)}} \over {(2)(1)}}$$
=>$$x = {{25 ± \sqrt{625 - 624}} \over {2}}$$
=>$$x = {{25 + 1} \over {2}} , {{25 - 1} \over {2}}$$
=>$$x = 13, 12$$
Therefore, Shefali’s marks in Mathematics = 13 or 12
Shefali’s marks in English = 30 – x = 30 – 13 = 17
Or Shefali’s marks in English = 30 – x = 30 – 12 = 18
Therefore, her marks in Mathematics and English are (13, 17) or (12, 18).