Age of Brook

If Colin is $x$ years old, then Brook is $2x$ and Peter is $2x+2$ years old. Totally $x+2x+(2x+2)=5x+2=27$ , so $5x=25$ and $x=5$ .

Brook is $2x=2*5=10$ years old.

Let the ages of Peter, Brook, and Colin be $P,$ $B$ and $C$ respectively.

Peter is $2$ years older than Brook,

$\Rightarrow$ $P = B + 2$

Brook is twice old as Colin,

$\Rightarrow B = 2C$

$\Rightarrow C =$ $\dfrac{B}{2}$

The total of their ages is $27$ years.

So,

$\Rightarrow B + 2 + B +$ $\dfrac{B}{2}$ $= 27$

$\Rightarrow 2B +$ $\dfrac{B}{2}$ $= 27 - 2 = 25$

$\Rightarrow$ $\dfrac{5}{2}$ $B = 25$

$\Rightarrow$ $\dfrac{25 \times 2}{5}$ = $\dfrac{50}{2}$ $= 10$

Therefore, $B = \boxed {10}$

suppose,

Colin is x. so, Brook is 2x and Peter is 2x+2

  so,   x+2x+2x+2=27

 or,x=25/5

or,x=5,      so,2x=5 x 2  =10= Brooks age

Let $P$ be the age of Peter, $B$ be the age of Brook and $C$ be the Colin. Then we have the three equations below

$P=2+B$ $\color{#D61F06}(1)$

$B=2C$ $\implies$ $C=\dfrac{B}{2}$ $\color{#D61F06}(2)$

$P+B+C=27$ $\color{#D61F06}(3)$

Substitute $\color{#D61F06}(1)$ and $\color{#D61F06}(2)$ in $\color{#D61F06}(3)$ .

$2+B+B+\dfrac{B}{2}=27$

$2.5B=25$

$\boxed{B=10}$