Question

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.

Answer 1

SOLUTION :  

Let the marks in Maths be x.

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

A.T.Q

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

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

⇒ -x² + 25x + 54 = 210

⇒ x² - 25x + 156 = 0

⇒ x² - 12x - 13x + 156 = 0

[By middle term splitting]

⇒ x(x - 12) -13(x - 12) = 0

⇒ (x - 12) (x - 13) = 0

⇒ (x - 12) = 0 or  (x - 13) = 0

⇒ x = 12  or x = 13

Case 1 :  

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

Case 2:  

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

Hence, the marks in Maths are (12,13) and marks in English are (18,17)

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Answer 2

Let her marks in Mathematics be x.
Then, her marks in English will be ( 30 - x ).

According to the question,

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

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

27x - x^2 + 54 - 2x = 210

25x - x^2 + 54 = 210

0 = x^2 - 25x - 54 + 210

0 = x^2 - 25x + 156

0 = x^2 - 13x - 12x + 156

0 = x ( x- 13 ) - 12 ( x - 13 )

0 = ( x - 12) ( x -13 )

( x - 12 ) = 0

x = 12

( x- 13 ) = 0

x = 13

$<h3>Marks of Mathematics = x = 12 </h3>$

$<h3>Marks of English = ( 30 - x ) = ( 30 - 12 ) = 18</h3>$

If x = 13,

$<h3>Then, Marks of mathematics = x = 13</h3>$

$<h3>Marks of English = ( 30 - x ) = 30 - 13 = 17</h3>$