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Let marks got by P in Mathematics = x Then, marks got by P in Science = (28 – x) Now, according to the given condition, we have (x + 3) (28 – x – 4) = 180 ⇒ (x + 3) (24 – x) = 180 ⇒ 24x – x 2 + 72 – 3x = 180 ⇒ –x 2 + 21x + 72 – 180 = 0 ⇒ –x 2 + 21x – 108 = 0 ⇒ x 2 – 21x + 108 = 0 ⇒ x 2 – 12x – 9x + 108 = 0 ⇒ x(x – 12)– 9 (x – 12) = 0 ⇒ (x – 12) (x – 9) = 0 ⇒ x = 12 or x = 9 Hence if marks got by P in mathematics 12 then marks got by him in science = 28 – 12 =16 Ans. And if marks got by P in mathematics 9 then Marks got by him in science = 28 – 9 = 19 Ans.

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202. In a class, 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 marks obtained in the two subjects would have been 180. Find the marks obtained in the two subjects seperately.

Let marks got by P in Mathematics = x
Then, marks got by P in Science = (28 – x)
Now, according to the given condition, we have
(x + 3) (28 – x – 4) = 180
⇒ (x + 3) (24 – x) = 180
⇒ 24x – x² + 72 – 3x = 180
⇒ –x² + 21x + 72 – 180 = 0
⇒ –x² + 21x – 108 = 0
⇒ x² – 21x + 108 = 0
⇒ x² – 12x – 9x + 108 = 0 ⇒ x(x – 12)– 9 (x – 12) = 0
⇒ (x – 12) (x – 9) = 0
⇒ x = 12
or x = 9
Hence if marks got by P in mathematics 12 then marks got by him in science = 28 – 12 =16 Ans.
And if marks got by P in mathematics 9 then
Marks got by him in science = 28 – 9 = 19 Ans.

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