Question

In a group one -third of the members are disciplined, the square root of total number of persons in the group are punctual and the remaning three are hard working. find the total number of persons in the group

Answer 1

Answer: The answer is 9.

Step-by-step explanation: Let the total number of persons in the group be 'x'.

According to the given information,

Number of disciplined persons is $\dfrac{1}{3}x.$

Number of punctual persons is $\sqrt{x}.$

And the rest 3 persons are hard working.

Formulating the given information mathematically, we have

$\dfrac{1}{3}x+\sqrt x+3=x\\\\\Rightarrow \sqrt x=x-\dfrac{1}{3}x-3\\\\\Rightarrow \sqrt x=\dfrac{2}{3}x-3\\\\\Rightarrow x=(\dfrac{2}{3}x-3)^2\\\\\Rightarrow x=\dfrac{4}{9}x^2-4x+9\\\\\Rightarrow 9x=4x^2-36x+81\\\\\Rightarrow 4x^2-36-9x+81=0\\\\\Rightarrow 4x(x-9)-9(x-9)=0\\\\\Rightarrow (x-9)(4x-9)=0.$

So,

$x-9=0~~\textup{or}~~4x-9 = 0\\\\\Rightarrow x=9~~\textup{or}~~x=\dfrac{9}{4}.$

Since the number of persons cannot be a fraction, so there are total 9 persons in the group.