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: 

${\displaystyle x+y=40}$                           ............(1) 

Also 

${\displaystyle (x+3)(y-4)=360}$ 

⇒(x+3)(40-x-4)=360       [from (1)] 

⇒${\displaystyle (x+3)(36-x)=360}$ 

⇒${\displaystyle 36x-x^2+108-3x=360}$ 

⇒${\displaystyle 33x-x^2-252=0}$ 

⇒${\displaystyle -x^2+x^2-252=0}$ 

⇒${\displaystyle x^2-33x-252=0}$ 

⇒${\displaystyle x^2-33x-252=0}$ 

⇒${\displaystyle x^2-(21x-12)x+252=0}$ 

⇒${\displaystyle x^2-21x-12x+252=0}$ 

⇒${\displaystyle x(x-21)-12(x-21)=0}$ 

⇒${\displaystyle (x-21)(x-12)=0}$ 

⇒${\displaystyle x=21 \text{or} x=12}$ 

If${\displaystyle x=21,}$ 

y=${\displaystyle 40-21=119}$ 

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

${\displaystyle Ifx=12,}$

${\displaystyle y=40-12=28}$ 

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