Question

In a class test, the sum of Kamal’s marks in mathematics and English is 40. Had he got 3 marks more in mathematics and 4 marks less in English, the product of the marks would have been 360. Find his marks in two subjects separately.

Answer 1

Let the marks of Kamal in mathematics and English be x and y, respectively. According to the question: 

`x+y=40`                           ............(1) 

Also 

`(x+3) (y-4)=360` 

⇒(x+3)(40-x-4)=360       [from (1)] 

⇒`(x+3)(36-x)=360` 

⇒`36x-x^2+108-3x=360` 

⇒`33x-x^2-252=0` 

⇒`-x^2+x^2-252=0` 

⇒`x^2-33x-252=0` 

⇒`x^2-33x-252=0` 

⇒`x^2-(21x-12)x+252=0` 

⇒`x^2-21x-12x+252=0` 

⇒`x(x-21)-12(x-21)=0` 

⇒`(x-21) (x-12)=0` 

⇒` x=21  or  x=12` 

If` x=21, ` 

y=`40-21=119` 

Thus, Kamal scored 21 and 19 marks in mathematics and English, respectively. 

`If x=12, `

`y=40-12=28` 

Thus, Kamal scored 12 and 28 marks in mathematics and English, respectively.