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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.
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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.
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