Q. 314.0( 11 Votes )

In a class test, the sum of Kamal's marks in mathematics and English is 40. Had he got 3 marks more in mathematics and 4 marks less in English, the product of the marks would have been 360. Find his marks in two subjects separately.

Answer :

Let Kamal's marks in mathematics and English be x and y, respectively

According to the question


x + y = 40 – – – – – – – (1)


Also (x + 3)(y – 4) = 360


(x + 3)(40 – x – 4) = 360 from (1)


(x + 3)(36 – x) = 360


36x – x2 + 108 – 3x = 360


33x – x2 – 252 = 0


x2 – 33x + 252 = 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 = – 33 c = 252


= 1. – 252 = 252


And either of their sum or difference = b


= – 33


Thus the two terms are – 21 and – 12


Sum = – 21 – 12 = – 33


Product = – 21. – 12 = 252


x2 – 33x + 252 = 0


x2 – 21x – 12x + 252 = 0


x(x – 21) – 12(x – 21) = 0


(x – 21) (x – 12) = 0


(x – 21) = 0 or (x – 12) = 0


x = 21 or x = 12


if x = 21


y = 40 – 21 = 19


Kamal's marks in mathematics and English are 21 and 19


if x = 12


y = 40 – 12 = 28


Kamal's marks in mathematics and English are 12 and 28


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