Explanation:

- Let's denote the original length as L and the original breadth as B.

- The area of the original rectangle is then \( L \times B \).

- In the new rectangle, the length is increased to 3 times, so it becomes \( 3L \).

- The breadth is decreased to half, so it becomes \( \frac{B}{2} \).

- The area of the new rectangle is \( 3L \times \frac{B}{2} = \frac{3LB}{2} \).

- The ratio of the original area to the new area is:

$$

\frac{LB}{\frac{3LB}{2}} = \frac{2LB}{3LB} = \frac{2}{3}

$$

- ? Option 1: 3 : 1 — Not correct

- Option 2: 2 : 3 — Correct

- ? Option 3: 1 : 3 — Not correct

- ? Option 4: 3 : 2 — Not correct