Question

In a class test, the sum of marks obtained by P in Mathematics and Science is 28. Had he got 3 more marks in Mathematics and 4 marks less in Science, the product of marks obtained in the two subjects would have been 180? Find the marks obtained in two subjects separately.

Answer 1

Let the marks obtained in mathematics be x then marks in science be 28-x 
acc,
(x+3)(28-x-4)=180
⇒(x+3)(24-x)=180
⇒24x-x²+72-3x=180
⇒21x-x²-180=0
⇒x²-21x+180=0
⇒x²-12x-9x+108=0
⇒x(x-12)-9(x-12)=0
⇒(x-9)(x-12)=0
∴x=9,12
the marks scored in maths can be 9 or 12
if she got 12 in maths then she got 28-12=16 in science
if she got 9 in maths then she got 28-9=19 in science