In a class test, the sum of Moulika’s marks in Mathematics and English is 30. If 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 the two subjects.
Answers
Mark of maths = x
Mark of English = 30 -x
According to question
(x+2) x (30-x+3) = 210
(x+2)(27 -x) = 210
-x^2 - 2x + 27x + 54 =210
x^2 - 25x +156 = 0
x^2 - 13x - 12x + 156 = 0
x(x-13) - 12(x-13) = 0
(x-12)(x-13)
x = 12, 13
Answer:
Case ( i ) Math marks ( x ) = 12 ,
and English marks ( y ) = 18
Case ( ii ) Maths marks ( x ) = 13
and English marks ( y ) = 17
Step-by-step explanation:
Let Mounikas marks in
Mathematics = x
Mounikas marks in English= y
Given that x + y = 30 ----( 1 )
( x + 2 )( y - 3 ) = 210
=> xy - 3x + 2y - 6 = 210
=> x( 30 - x )-3x+2( 30 - x ) -6=210
=> 30x - x² - 3x +60-2x-6= 210
=> x² - 25x + 156 = 0
=> x² - 12x - 13x + 156 = 0
=> x( x - 12 ) - 13( x - 12 ) = 0
=> ( x - 12 )( x - 13 ) = 0
Therefore,
x - 12 = 0 or x - 13 = 0
x = 12 or x = 13
Case ( i )
If x = 12 then y = 30 - x = 30-12=18
Therefore ,
Math marks ( x ) = 12 and
English marks ( y ) = 18
Case ( ii ),
If x = 13 then y = 30 - x = 30-13=17
Therefore ,
Math marks ( x ) = 13 and
English marks ( y ) = 17
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