In a class test, Raveena got a total of 30 marks in English and Mathematics. Had she got 2 more marks in mathematics and 3 marks less in English, then the product of her marks obtained would have been 210. Find the individual marks obtained in the two subjects.

Let the marks in Mathematics = x

So, the marks in English = 30 – x

Let the new marks in Mathematics = x + 2

And the new marks in English = 30 – x – 3 = 27 – x

Given, with the new marks, the product of marks obtained = 210

So, (x + 2) (27 – x) = 210

⇒ 27x – x² + 54 – 2x = 210

⇒ -x² + 25x + 54 – 210 = 0

⇒ -x² + 25x – 156 = 0

⇒ x² – 25x + 156 = 0

⇒ x² – 13x – 12x + 156 = 0

By factorisation method,

⇒ x (x – 13) – 12(x – 13) = 0

⇒ (x – 13) (x – 12) = 0

⇒ x – 13 = 0 (or) x – 12 = 0

⇒ x = 13 (or) x = 12 (Marks in Mathematics)

Marks in English = 30 – x

= 30 – 13 (or) 30 – 12

= 17 (or) 18

Answer: Raveena’s marks in Mathematics and English are 13 and 17 (or) 12 and 18 respectively.