AP EAMCET Engineering 23 Sep 2020 Shift 1 Paper

Given,
Number of blue balls =5
Number of balls =x
Total number of balls =5+x
Total number of balls =5+x
Number of ways of drawing 2 blue balls =‌5C2
Number of ways of drawing 2 balls =‌(5+x)C2
Given,
P( drawing 2 blue balls )=‌

5

14

⇒‌‌‌

‌5C2

(5+x)C2

=‌

5

14

⇒‌‌‌

10

(5+x)(4+x) 2×1

=‌

5

14

⇒‌‌‌

20

x2+9x+20

=‌

5

14

⇒‌‌x2+9x+20=56
⇒‌‌x2+9x−36=0
⇒‌‌x2+12x−3x−36=0
⇒‌‌x(x+12)−3(x+12)=0
⇒‌‌x=3
( ∵ Number of balls can not be negative.)