At t = 0 , a particle has a velocity u towards east. Its...

Let the initial velocity be $u$ towards east and the constant acceleration be $a$ towards west. Taking east as the positive direction, the velocity is $u$ and acceleration is $-a$.

The displacement of the particle at time $t$ is given by $s = ut - \dfrac{1}{2}at^2$.

The magnitude of displacement in the first $10$ seconds is:
$x_A = |s(10) - s(0)| = |10u - 50a|$

The magnitude of displacement in the subsequent $10$ seconds is:
$x_B = |s(20) - s(10)| = |(20u - 200a) - (10u - 50a)| = |10u - 150a|$

Comparing $x_A$ and $x_B$ for different values of $u$ and $a$:
Case 1: If $u = 20$ and $a = 1$, $x_A = |200 - 50| = 150$ and $x_B = |200 - 150| = 50$. Here, $x_A > x_B$.

Case 2: If $u = 10$ and $a = 1$, $x_A = |100 - 50| = 50$ and $x_B = |100 - 150| = 50$. Here, $x_A = x_B$.

Case 3: If $u = 5$ and $a = 1$, $x_A = |50 - 50| = 0$ and $x_B = |50 - 150| = 100$. Here, $x_A < x_B$.

Since the relation between $x_A$ and $x_B$ depends on the specific values of initial velocity and acceleration, the provided information is insufficient to determine a unique relation.