1. **Problem statement:** We need to find the width of a rectangular plot where the length and width are in the ratio 2:1, and the total cost of fencing the plot is 1500. The cost per meter of fencing is 50. 2. **Formula and explanation:** The cost of fencing is calculated by multiplying the perimeter of the plot by the cost per meter. The perimeter $P$ of a rectangle is given by: $$P = 2(\text{length} + \text{width})$$ Given the ratio of length to width is 2:1, let the width be $x$ meters. Then the length is $2x$ meters. 3. **Calculate the perimeter:** $$P = 2(2x + x) = 2(3x) = 6x$$ 4. **Calculate the total cost:** Cost = Perimeter $\times$ Cost per meter $$1500 = 6x \times 50$$ 5. **Solve for $x$:** $$1500 = 300x$$ $$x = \frac{1500}{300} = 5$$ 6. **Answer:** The width of the plot is $5$ meters.