1. **State the problem:** We have a room where the length is $\frac{3}{2}$ times the breadth. The cost of carpeting the floor is 17550 at 3.25 per m², and the cost of papering the walls is 240.80 at 1.40 per m². One door and two windows occupy 8 m². We need to find the dimensions of the room. 2. **Define variables:** Let the breadth be $b$ meters. Then the length is $l = \frac{3}{2}b$ meters. 3. **Floor area and carpeting cost:** Floor area $= l \times b = \frac{3}{2}b \times b = \frac{3}{2}b^2$ Cost of carpeting $= 3.25 \times$ floor area $= 17550$ 4. **Calculate floor area:** $$3.25 \times \frac{3}{2}b^2 = 17550$$ $$\frac{3}{2}b^2 = \frac{17550}{3.25}$$ $$\frac{3}{2}b^2 = 5400$$ 5. **Solve for $b^2$:** $$b^2 = \frac{5400 \times 2}{3} = 3600$$ $$b = \sqrt{3600} = 60 \text{ meters}$$ 6. **Find length $l$:** $$l = \frac{3}{2} \times 60 = 90 \text{ meters}$$ 7. **Calculate wall area for papering:** Height $h$ is unknown. Walls area without door and windows: $$2h(l + b) - 8$$ Cost of papering: $$1.40 \times (2h(l + b) - 8) = 240.80$$ 8. **Solve for $h$:** $$2h(90 + 60) - 8 = \frac{240.80}{1.40}$$ $$2h \times 150 - 8 = 172$$ $$300h - 8 = 172$$ $$300h = 180$$ $$h = \frac{180}{300} = 0.6 \text{ meters}$$ **Final answer:** The dimensions of the room are: - Breadth = 60 meters - Length = 90 meters - Height = 0.6 meters