Question

In a group one-third of the members are disciplined,The square root of the total no. of persons in the group are punctual and the remaining 3 are hard working.Find the total no. of persons in the group

Answer 1

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Answer 2

Answer:

The total number of members in the group are 9.

Step-by-step explanation:

Let the total number of members in the group = x

Now, 'One-third of the members are disciplined'.

So, the number of members disciplined = $\frac{x}{3}$

Also, number of members punctual = $\sqrt{x}$

Plus, the remaining 3 are hard working members.

So, we have the relation,

$x=\frac{x}{3}+\sqrt{x}+3$

i.e. $x-\frac{x}{3}-3=\sqrt{x}$

i.e. $\frac{2x}{3}-3=\sqrt{x}$

Squaring both sides, we get,

i.e. $(\frac{2x}{3}-3)^2=x$

i.e. $\frac{4x^2}{9}+9-4x=x$

i.e. $\frac{4x^2}{9}+9-5x=0$

i.e. $4x^2-45x+81=0$

i.e. $(x-2.25)(x-9)=0$

i.e. x= 2.25 and x= 9

Since, x represents the number of members in the group. So, it has to be a whole number.

Thus, x= 9.

That is, the total number of members in the group are 9.