Question

In a class test, the sum of the 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 by him in the two subjects separately.

Answer 1

Let the marks obtained by P in mathematics and science be x and (28- x) respectively. According to the given condition,  

`(x+3)(28-x-4)=180`

⇒`(x+3) (24-x)=180` 

⇒`-x^2+21x+72=180` 

⇒`x^2-21x+180` 

⇒`x^2-12x+9x+108=0` 

⇒`x(x-12)-9(x-12)=0` 

⇒`(x-12) (x-9)=0` 

⇒`x-12=0  or  x-9=0` 

⇒`x=12  or  x=9` 

When `x=12` 

`28-x=28-12=16` 

When `x=9` 

`28-x=28-9=19`

Hence, he obtained 12 marks in mathematics and 16 marks in science or 9 marks in mathematics and 19 marks in science.