Q. 354.2( 10 Votes )

In a class test, the sum of the marks obtained by P in mathematics and science is 28. Had he got 3 more marks in mathematics and 4 marks less in science, the product of marks obtained in the two subjects would have been 180. Find the marks obtained by him in the two subjects separately.

Answer :

Let the marks obtained by P in mathematics and science be x and (28 – x) respectively

According to the given condition,


(x + 3)(28 – x – 4) = 180


(x + 3)(24 – x) = 180


– x2 + 21x + 72 = 180


x2 – 21x + 108 = 0


Using the splitting middle term – the middle term of the general equation is divided in two such values that:


Product = a.c


For the given equation a = 1 b = – 21 c = 108


= 1.108 = 108


And either of their sum or difference = b


= – 21


Thus the two terms are – 12 and – 9


Difference = – 12 – 9 = – 21


Product = – 12. – 9 = 108


x2 – 12x – 9x + 108 = 0


x (x – 12) – 9 (x – 12) = 0


(x – 12) (x – 9) = 0


(x – 12) = 0 or (x – 9) = 0


x = 12, x = 9


When x = 12,


28 – x = 28 – 12 = 16


When x = 9,


28 – x = 28 – 9 = 19


Hence he obtained 12 marks in mathematics and 16 science or


He obtained 9 marks in mathematics and 19 science.


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