Q. 54.4( 248 Votes )
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.
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.
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
⇒ 27a -a2 + 54 - 2a = 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 12
marks in english is 30 - a = 30 - 12 = 18
If marks in mathematics is 13
marks in english is 30 - a = 30 - 13 = 17
Marks in Mathematics = 12, Marks in English = 18
Marks in Mathematics = 13, Marks in English = 17
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