Question

From a group of 2x² black bees, square root of half of the group went to a tree. Again eight-ninth of the bees went to the same tree. The remaining two got caught up in a fragrant lotus. How many bees were there in total?

Answer 1

Total numbers of black bees = 2x² 

Half of the group = `1/2 xx 2x^2` = x²

Square root of half of the group = `sqrt(x^2)` = x

Eight – ninth of the bees = `8/9 xx 2x^2 = (16x^2)/9`

Number of bees in the lotus = 2

By the given condition

`x + (16x^2)/9 + 2` = 2x² 

9x + 16x² + 18 = 18x²  ...(Multiply by 9)

18x² – 16x² – 9x – 18 = 0 ⇒ 2x² – 9x – 18 = 0

2x² – 12x + 3x – 18 = 0

2x(x – 6) + 3 (x – 6) = 0

(x – 6) (2x + 3) = 0

x – 6 = 0 or 2x + 3 = 0

x = 6 or 2x = – 3 ⇒ x = `(-3)/2`   ...(number of bees will not be negative)

Total number of black bees = 2x² = 2(6)² 

= 72