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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 Two Subjects. - CBSE Class 10 - Mathematics

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Question

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 two subjects.

Solution

Let marks obtained by P in mathematics be x, then in science = (28 - x)

It is given that,

(x + 3) x (28 - x - 4) = 180

(x + 3) x (24 - x) = 180

24x - x2 + 72 - 3x = 180

-x2 + 21x + 72 - 180 = 0

- (x2 - 21x - 72 + 180) = 0

x2 - 21x + 108 = 0

x2 - 12x - 9x + 108 = 0

x(x - 12) - 9(x - 12) = 0

(x - 12)(x - 9) = 0

x - 12 = 0

x = 12

Or

x - 9 = 0

x = 9

Therefore, when x = 12 then

28 - x = 28 - 12 = 16

Hence, marks in mathematics 12 and marks in science 16.

Or, when x = 9 then

28 - x = 28 - 9 = 19

Hence, marks in mathematics 9 and marks in science 19.

  Is there an error in this question or solution?

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Solution 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 Two Subjects. Concept: Solutions of Quadratic Equations by Factorization.
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