(Q23)In a class test, the sum of Moulika's marks in Mathematics and English is 30. If she got 2 marks more in Mathematics and 3 marks less in English, the product of her marks would have been 210. Find her marks in the two subjects.

Sum of the marks in mathematics and English = 30

Let Moulika's marks in Mathematics be x Then her marks in English = 30 - x

If she got 2 more marks in Mathematics, then her marks would be = x + 2.

If she got 3 marks less in English then her marks wolud be 30 - x - 3 = 27 - x

By problem (x + 2)(27 - x) = 210

x(27 - x) + 2(27 - x) = 210

27x - x² + 54 - 2x = 210

-x² + 25x + 54 = 210

x² - 25x - 54 + 210 = 0

x² - x - 13x + 156 = 0

x(x - )- 13(x - )

(x - )(x - 13) = 0

x - = 0 or x - 13 = 0

x = or x = 13

If x = , then marks in Mathematics = 12 and English = 30 - = .

If x = 13, then marks in Mathematics = 13 and English = 30 - 13 = 17