In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects

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#### Solution

Let the marks in Maths be x.

Then, the marks in English will be 30 - x.

According to the question,

(x + 2)(30 - x - 3) = 210

(x + 2)(27 - x) = 210

⇒ -x^{2} + 25x + 54 = 210

⇒ x^{2} - 25x + 156 = 0

⇒ x^{2} - 12x - 13x + 156 = 0

⇒ x(x - 12) -13(x - 12) = 0

⇒ (x - 12)(x - 13) = 0

⇒ x = 12, 13

If the marks in Maths are 12, then marks in English will be 30 - 12 = 18

If the marks in Maths are 13, then marks in English will be 30 - 13 = 17

Concept: Solutions of Quadratic Equations by Factorization

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