Given: In a class test, the sum of the marks obtained by P in Mathematics and science is 28. Had he got 3 marks more in Mathematics and 4 marks less in Science. The product of his marks, would have been 180.

To find: his marks in the two subjects.

Solution: Let the marks obtained in Mathematics by P be ‘a’

Given, sum of the marks obtained by P in Mathematics and science is 28.

⇒ Marks obtained in science = 28 – a

Also, if he got 3 marks more in Mathematics and 4 marks less in Science, product of his marks, would have been 180.

⇒ (a + 3)(28 – a – 4) = 180

⇒ (a + 3)(24 – a ) = 180

⇒ 24a - a² + 72 - 21a = 180

⇒ -a² + 21a + 72 = 180

⇒ -a² + 21a + 72 - 180 = 0

⇒ -a² + 21a - 108 = 0

⇒ a² – 21a + 108 = 0

Factorise the above quadratic equation by splitting the middle term:

⇒ a² – 12a – 9a + 108 = 0

⇒ a(a – 12) – 9(a – 12) = 0

⇒ (a – 9)(a – 12) = 0

⇒ a = 9 or 12If marks obtained in mathematics is 9, the marks obtained in science is 28-a = 28 - 9 = 19

⇒ Marks in Mathematics = 9, Marks in Science = 19

Or

If marks obtained in mathematics is 12, the marks obtained in science is 28-a = 28 - 12 = 16

Marks in Mathematics = 12, Marks in Science = 16