 Hello friends, welcome to the session. I am Alka and today we are going to discuss a question which is In a class test the sum of Shivali's marks in mathematics and English is 30 Had she got two marks more in mathematics and three marks less in English the product of their marks would have been 210. Find her marks in the two subjects. Now, let's start with the solution Here are two unknown things First is Shivali's marks in mathematics and second is Shivali's marks in English. So first of all let us assume them So let Shivali's marks in mathematics equal to x and Shivali's marks in English equal to 30 minus x Since we know that some of the marks is 30. Now according to the question If she had two more marks in mathematics and three marks less in English Then the product of marks would be equal to 210. Therefore, we can write x plus 2 and 30 minus x minus 3 equal to 210 This implies x plus 2 into 27 minus x equal to 210 Which can be written as minus x plus 2. We have taken minus common from here. This gives us x minus 27 equal to 210. Now on further simplifying it we get x square minus 25x minus 54 equal to 210. This implies minus x square plus 25x plus 54 equal to 210 This implies x square minus 25x minus 54 plus 110 equal to 0 This implies x square minus 25x plus 156 equal to 0 This implies x square now will split the middle term. We get x square minus 13x minus 12x plus 156 equal to 0 This implies x common x minus 13 and from these two terms we will take minus 12 common and get x minus 13 equal to 0. This implies x minus 13 into x minus 12 equal to 0. Therefore, we can say x equal to 13 or x equal to 12. Now we see that marks in mathematics are 13 or 12. Now when x equal to 13 then marks in English will be equal to 30 minus 13 that is 17. Similarly, when x equal to 12 that is marks in mathematics equal to 12 then marks in English equal to 30 minus 12 that is 18. Hence marks in mathematics equal to 12 and marks in English equal to 18 and when marks in mathematics are 13 then marks in English equal to 17 which is a required solution. Hope you understood it and enjoyed the session. Goodbye and take care.