correct answer is: a) 12\;:\;5

Explanation

According to the question,
3 steps of the police = 6 steps of the thief
\therefore 1 step of the police = \large\frac{6}{3} steps of the thief
\therefore 6 steps of the police = \large\left(\frac{6\times6}{3}\right) steps of the thief
\rightarrow 12 steps of the thief.
Now, in the same time, the policeman moves 6 steps and the thief moves 5 steps.
\therefore The ratio of their speeds :
\rightarrow\large\frac{6\ steps\ of\ the\ police}{5\ steps\ of\ the\ thief}
\rightarrow\large\frac{12\ steps\ of\ the\ theif}{5\ steps\ of\ the\ thief} _{[6 steps police = 12 steps thief]}
\rightarrow\large\frac{12}{5} or 12\;:\;5
Ans: The ratio of their speeds is 12\;:\;5\;.

Other variants of this particular math question are:

1. When a thief moves 5 steps, a policeman follows with 6 steps. Additionally, if the policeman travels 3 steps, it equals the distance covered by 6 steps of the thief. What is the ratio of their speeds?
2. Pursuing a thief, a police officer follows a pattern: for every 5 steps taken by the thief, the officer strides 6 steps. Moreover, if the officer advances 3 steps, it equals the distance covered by 6 steps of the thief. Determine the ratio of their speeds.
3. A thief is pursued by a policeman. As the thief advances 5 steps, the policeman covers 6 steps in pursuit. Also, when the policeman moves 3 steps, it matches the distance of 6 steps by the thief. Compute the ratio of their speeds.