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:

\(\Rightarrow \) \((x + 2) (27 - x) = 210\)
\(\Rightarrow \) \(27x - x^2 + 54 - 2x = 210\)
\(\Rightarrow \) \(x^2 - 25x + 156 = 0\)

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 = \(x = {{-b ± \sqrt{b^2 - 4ac}} \over {2a}}\)

\(\Rightarrow \) \(x = {{25 ± \sqrt{(25)^2 - 4(1)(156)}} \over {(2)(1)}}\)
\(\Rightarrow \) \(x = {{25 ± \sqrt{625 - 624}} \over {2}}\)
\(\Rightarrow \) \(x = {{25 + 1} \over {2}} , {{25 - 1} \over {2}}\)
\(\Rightarrow \) \(x = 13, 12\)

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).