Question.
In a class test, the sum of Shefali's marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.
In a class test, the sum of Shefali's marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.
Solution:
Let the marks in Maths be x.
Then, the marks in English will be 30 – x.
According to the given question,
(x+2)(30-x-3)=210
$(x+2)(27-x)=210$
$\Rightarrow-x^{2}+25 x+54=210$
$\Rightarrow x^{2}-25 x+156=0$
$\Rightarrow x^{2}-12 x-13 x+156=0$
$\Rightarrow x(x-12)-13(x-12)=0$
$\Rightarrow(x-12)(x-13)=0$
$\Rightarrow x=12,13$
If the marks in Maths are 12, then marks in English will be 30 – 12 = 18
If the marks in Maths are 13, then marks in English will be 30 – 13 = 17.
Let the marks in Maths be x.
Then, the marks in English will be 30 – x.
According to the given question,
(x+2)(30-x-3)=210
$(x+2)(27-x)=210$
$\Rightarrow-x^{2}+25 x+54=210$
$\Rightarrow x^{2}-25 x+156=0$
$\Rightarrow x^{2}-12 x-13 x+156=0$
$\Rightarrow x(x-12)-13(x-12)=0$
$\Rightarrow(x-12)(x-13)=0$
$\Rightarrow x=12,13$
If the marks in Maths are 12, then marks in English will be 30 – 12 = 18
If the marks in Maths are 13, then marks in English will be 30 – 13 = 17.