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.

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 – x^{2} + 108 – 3x = 360

33x – x^{2} – 252 = 0

x^{2} – 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

x^{2} – 33x + 252 = 0

x^{2} – 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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