A proton has three quarks. Let there be n up quarks in a proton, each having a charge of $(+2 / 3)e$.

Charge due to $n$ up quarks $=\left(\frac{2}{3} e\right) n$

Number of down quarks in a proton $=3-n$

Each down quark has a charge of $-\frac{1}{3} e$

Charge due to $(3- n )$ down quarks $=\left(-\frac{1}{3} e\right)(3-n)$

Total charge on a proton $=+e$

$\therefore e=\left(\frac{2}{3} e\right) n+\left(-\frac{1}{3} e\right)(3-n)$

$\Rightarrow e=\frac{2 n e}{3}-e+\frac{n e}{3}$$\Rightarrow 2 e=n e \Rightarrow n=2$

Number of up quarks in a proton, $n=2$ Number of down quarks in a proton $=3-n=3-2=1$

Therefore, a proton can be represented as '$uud$'.

A neutron also has three quarks. Let there be $n$ up quarks in a neutron.

Charge on a neutron due to $n$ up quarks $=\left(+\frac{2}{3} e\right) n$

Number of down quarks is $3-n$, and each having a charge of $-\frac{1}{3} e$.

Charge on a neutron due to $(3-n)$ down quarks $=\left(-\frac{1}{3} e\right)(3-n)$

Total charge on a neutron $=0$

$\therefore 0=\left(\frac{2}{3} e\right) n+\left(-\frac{1}{3} e\right)(3-n)$

$\Rightarrow 0=\frac{2 n e}{3}-e+\frac{n e}{3}$$\Rightarrow e=n e \Rightarrow n=1$

Number of up quarks in a neutron, $n=1$ Number of down quarks in a neutron $=3-n=2$ Therefore, a neutron can be represented as '$udd$'.