 Hi and welcome to the session. Today I will help you with the following question with scenes. In a class test, the sum of the marks obtained by P in Mathematics and Science is 28. Had we got three more marks in Mathematics and four marks less in Science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained in the two subjects separately. Let us proceed with its solution. In this question, we need to find the marks obtained in the two subjects that is in Mathematics and in Science and we are given that the sum of the marks obtained by P in Mathematics and Science is 28. So that means if we assume that the marks obtained in any one of the subject, same Mathematics is x, then the marks obtained in Science will be 28 minus x. So here first of all we will assume that the marks obtained by P in Mathematics px, then the marks obtained by P in Science will be 28 minus x because sum of marks obtained Mathematics and Science 28. Now we are given that had he got three more marks in Mathematics and four marks less in Science, the product of the marks obtained in the two subjects would have been 180. So according to the question, we have got three marks more in Mathematics that is the marks in Mathematics would have been x plus three and four marks less in Science. So the marks in Science would have been 28 minus x minus four, then the product of the marks obtained in the two subjects would have been 180. So here we got this equation and now we will solve this equation to get the value of x. So first of all this implies x plus three into here 28 minus four will be 24. So 24 minus x is equal to 180. Now let us multiply these brackets and we will get 24x plus 72 minus x square minus 3x is equal to 180. So this implies minus x square plus 21x is equal to 180 minus 72 which is equal to 108. And now this gives x square minus 21x plus 108 is equal to 0. Now to solve this quadratic equation, we will split its middle term that is minus 21x. So this will give us x square minus 9x minus 12x plus 108 is equal to 0. Here minus 9x into minus 12x is equal to 108x square and minus 9x plus minus 12x is equal to minus 21x. Now from the first two terms let us take x common. So this implies x into x minus 9. Now from the last two terms we will take minus 12th common. So we are left with x minus 9 equal to 0. Now from this we will take x minus 9 as common and we will get x minus 9 into x minus 12 is equal to 0. So from this we have x minus 9 will be equal to 0 or x minus 12 will be equal to 0 that is x will be equal to 9 or x will be equal to 12. Now we assumed x as the marks obtained in mathematics. So marks obtained by P in mathematics will be equal to 9 or 12. So here we have two cases. Case one is if marks obtained in mathematics is 9 then the marks obtained in science will be 28 minus 9 that is 19 and second case if the marks obtained in mathematics is 12 then the marks obtained in science will be 28 minus 12 which will be equal to 16. Thus in this question the marks obtained by P in mathematics and science will be 9 and 19 or 12 and 16. Thus here we have found the marks obtained by P in both the subjects separately. With this we finish this session. Hope you must have understood the question. Goodbye, take care and have a nice day.