#### 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.

#### Solution

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 - x^{2} + 72 - 3x = 180

-x^{2} + 21x + 72 - 180 = 0

- (x^{2} - 21x - 72 + 180) = 0

x^{2} - 21x + 108 = 0

x^{2} - 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.