1. Use the radius formula in a magnetic field

For a charged particle moving perpendicular to a uniform magnetic field,

$r = \frac{mv}{qB}$

2. Relate velocity to kinetic energy

Given both particles have the same kinetic energy,

$\frac{1}{2}mv^2 = K$

So,

$v = \sqrt{\frac{2K}{m}}$

Substitute into the radius formula:

$r = \frac{m}{qB}\sqrt{\frac{2K}{m}}$

$r = \frac{\sqrt{2Km}}{qB}$

Since $K$ and $B$ are same for both particles,

$r \propto \frac{\sqrt{m}}{q}$

3. Write the ratio of radii

Thus,

$\frac{r_1}{r_2} = \frac{\sqrt{m_1}/q_1}{\sqrt{m_2}/q_2} = \sqrt{\frac{m_1}{m_2}}\cdot \frac{q_2}{q_1}$

Given:

$\frac{r_1}{r_2} = \frac{6}{5}, \qquad \frac{m_1}{m_2} = \frac{9}{4}$

So,

$\frac{6}{5} = \sqrt{\frac{9}{4}}\cdot \frac{q_2}{q_1}$

$\frac{6}{5} = \frac{3}{2}\cdot \frac{q_2}{q_1}$

Hence,

$\frac{q_2}{q_1} = \frac{6}{5}\cdot \frac{2}{3} = \frac{4}{5}$

Therefore,

$\frac{q_1}{q_2} = \frac{5}{4}$

4. Match with options

So the ratio of their charges is

$5:4$

This matches Option B.