Question

Question 5 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.

Class 10 - Math - Quadratic Equations Page 88

Answer 1

Let the marks in Maths be x.
Then, the marks in English will be 30 - x.
According to the question,
(x + 2)(30 - x - 3) = 210
(x + 2)(27 - x) = 210
⇒ -x2 + 25x + 54 = 210
⇒ x2 - 25x + 156 = 0
⇒ x2 - 12x - 13x + 156 = 0
⇒ x(x - 12) -13(x - 12) = 0
⇒ (x - 12)(x - 13) = 0
⇒ x = 12, 13
If the marks in Maths are 12, then marks in English will be 30 - 12 = 18
If the marks in Maths are 13, then marks in English will be 30 - 13 = 17

Answer 2

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

===================================