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.
To find: Marks in two subjects
Method Used:
To solve the quadratic equation by factorisation method, follow the steps:
1) Multiply the coefficient of x2 and constant term.
2) factorise the result obtained in step 1.
3) Now choose the pair of factors in such a way that after adding or subtracting(splitting) them
You get coefficient of x.
Explanation:
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
If marks obtained is Mathematics is 9,
Marks in science = 28 – a
= 28 – 9
= 19
And
If marks obtained is Mathematics is 12,
Marks in science = 28 – a
= 28 – 12
= 16
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