Correct answer is: c) A\;:\;C\;=\;1\;:\;3\;.

Explanation

Here, the given ratio are :
A\;:\;B\;=\;2\;:\;3 or \large\frac{2}{3}
B\;:\;C\;=\;1\;:\;2 or \large\frac{1}{2}
Now, multiply all the equation :
\large\frac{A}{B}\times\frac{B}{C}\normalsize=\large\frac{2}{3}\times\frac{1}{2}
\rightarrow\large\frac{A}{C}\normalsize=\large\frac{1}{3}
\therefore A\;:\;C\;=\;1\;:\;3
Ans: A\;:\;C\;=\;1\;:\;3\;.

You can find this math problem in different styles like:

1. Given A:B = 2:3 and B:C = 1:2, determine the value of A:C.
2. If the ratio of A to B is 2:3 and the ratio of B to C is 1:2, what is the ratio of A to C?
3. A:B = 2:3 and B:C = 1:2, calculate the ratio of A to C.