Question

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 two subjects.

Answer 1

Let marks obtained by P in mathematics be x, then in science = (28 - x)

It is given that,

(x + 3) x (28 − x − 4) = 180

(x + 3) x (24 − x) = 180

24x − x² + 72 − 3x = 180

−x² + 21x + 72 − 180 = 0

− (x² − 21x − 72 + 180) = 0

x² − 21x + 108 = 0

x² − 12x − 9x + 108 = 0

x(x − 12) − 9(x − 12) = 0

(x − 12)(x − 9) = 0

x − 12 = 0

x = 12

Or

x − 9 = 0

x = 9

Therefore, when x = 12 then

28 − x = 28 − 12 = 16

Hence, marks in mathematics 12 and marks in science 16.

Or, when x = 9 then

28 − x = 28 − 9 = 19

Hence, marks in mathematics 9 and marks in science 19.