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 us say, the marks of Shefali in Maths be x.

Then, the marks in English will be 30 – x.

As per the given question,

$\left( x~+\text{ }2 \right)\left( 30\text{ }~x~\text{ }3 \right)\text{ }=\text{ }210$

$\left( x~+\text{ }2 \right)\left( 27\text{ }~x \right)\text{ }=\text{ }210$

$\Rightarrow -{{x}^{2}}~+\text{ }25x~+\text{ }54\text{ }=\text{ }210$

$\Rightarrow ~{{x}^{2}}~\text{ }25x~+\text{ }156\text{ }=\text{ }0$

$\Rightarrow ~{{x}^{2}}~~12x~\text{ }13x~+\text{ }156\text{ }=\text{ }0$

$\Rightarrow ~x\left( x~\text{ }12 \right)\text{ }-13\left( x~\text{ }12 \right)\text{ }=\text{ }0$

$\Rightarrow \left( x~\text{ }12 \right)\left( x~\text{ }13 \right)\text{ }=\text{ }0$

$\Rightarrow ~x~=\text{ }12,\text{ }13$

Therefore, if the marks in Maths are 12, then marks in English will be $30\text{ }\text{ }12\text{ }=\text{ }18$ and the marks in Maths are 13, then marks in English will be $30\text{ }\text{ }13\text{ }=\text{ }17$ .