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 their marks would have been 210 . Find her marks in the two subjects




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Answer 1

Let the marks in maths be = x

The marks in english will be = 30 - x

shefali got 2 marks more in mathematics = x + 2

And 3 marks less in english is ( 30 - x - 3 )

product of shefali's marks = 210

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

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

27x + 54 - x² - 2x = 210

- x² + 25x + 54 = 210

x² - 25x + 210 - 54 = 0

x² - 25x + 156 = 0

x² - 13x - 12x + 156 = 0

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

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

x - 13 = 0 or x - 12 = 0

x = 13 or x = 12

shefali's marks in mathematics = 13

marks in english = 30 - 13 = 17

or shefali's marks in mathematics = 12

marks in english = 30 - 12 = 18

hope this helps you

Answer 2

Answer:

Let ,

Shefali got in math= x number

.°. in English = 30 - x number

A/Q,

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

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

=> 27x - x² + 54 - 2x = 210

=> - x² + 25x + 54 = 210

=> - x² + 25x - 156 = 0

=> x² - 25x + 156 = 0

here a = 1 , b= - 25 , c= 156

.°. x = - ( -25 ) ± √(-25)² - 4 × 1 × 156/ 2 × 1

= 25 ± √625 - 624/ 2

= 25 ± √1/ 2

= 25 ± 1 /2

.°. x = 25+1/2 and 25 - 1/2

= 13 and 12

while x = 13

shefalis math number is = 13

and English number is = 30 - 13 = 17

when

x = 12

shefalis math number is = 12

and English number is = 30 - 12 = 18

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