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 her marks would have been 210. Find her marks in two subjects. (CBSE 2014)
Given : 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 her marks would have been 210.
To find: her marks in two subjects.
Solution:
Let the marks obtained in Mathematics by Shefali be ‘a’.
Given, sum of the marks obtained by Shefali in Mathematics and English is 30.
Marks obtained in english = 30 – a
Also, she got 2 marks more in Mathematics and 3 marks less in English, the product of her marks would have been 210.
⇒ (a + 2)(30 – a – 3) = 210
⇒ (a + 2)(27 – a ) = 210
⇒ -a2 + 25a + 54 = 210
⇒ -a2 + 25a + 54 - 210 = 0
⇒ -a2 + 25a - 156 = 0
⇒ a2 – 25a + 156 = 0
In factorization, we write the middle term of the quadratic equation either as a sum of two numbers or difference of two numbers such that the equation can be factorized.⇒ a2 – 13a – 12a + 156 = 0
⇒ a(a – 13) – 12(a – 13) = 0
⇒ (a – 12)(a – 13) = 0
⇒ a = 12 or 13
If marks in mathematics is 12marks in english is 30 - a = 30 - 12 = 18
If marks in mathematics is 13
marks in english is 30 - a = 30 - 13 = 17
Hence
Marks in Mathematics = 12, Marks in English = 18
Or
Marks in Mathematics = 13, Marks in English = 17
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