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. Find his marks in the two subjects.
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
⇒ -a2 + 21a + 72 = 180
⇒ a2 – 21a + 108 = 0
⇒ a2 – 12a – 9a + 108 = 0
⇒ a(a – 12) – 9(a – 12) = 0
⇒ (a – 9)(a – 12) = 0
⇒ a = 9 or 12
Thus, marks obtained in science = 19 or 16
Marks in Mathematics = 12, Marks in Science = 16
Or
Marks in Mathematics = 9, Marks in Science = 19