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 subject​

Answer 1

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

Answer 2

Given:

• The sum of Shefali’s marks in Mathematics and English is 30.

• She had got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210.

To find out:

Find her marks in the two subject?

Solution:

Let marks in Mathematics = x

And marks in English = y

According to given conditions,

x + y = 30 => y = 30 - x ................ ( 1 )

And, ( x + 2 ) ( y - 3 ) = 210 ...................( 2 )

From ( 1 ) and ( 2 ), we have

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

⇒ ( x + 2 ) ( 27 - x ) = 210

⇒ 27x - x² + 54 - 2x = 210

⇒ 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

When x = 13 , y = 17

When x = 12 , y = 18

Hence, marks in Mathematics are 13 and in English are 17 or marks in Mathematics are 12 and in English are 18 .