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प्रश्न
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?
उत्तर
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
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