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.

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

– x^{2} + 21x + 72 = 180

x^{2} – 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

x^{2} – 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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