Question

In a class test, the sum of 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 in two subjects separately.​

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

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Answer

Let P has obtained x in mathematics and y in science.

Then by the problem,

x+y=28(1).

If P would have got 3 marks more in mathematics, then P would have got (x+3) in mathematics and if P would have got 4 marks less in science then P would have got (y−4) in science.

Also

(x+3)(y−4)=180

or, (x+3)(24−x)=180

or, 72+21x−x

2

=180

or, x

2

−21x+108=0

or (x−12)(x−9)=0

or, x=12,9⇒y=16,19.

There may be two situation.

P obtained 12 marks in mathematics and 16 in science.

or,

P obtained 9 marks in mathematics and 19 in science.