1. **Problem Statement:** A rectangular pond has a length of 75 metres and a breadth of 50 metres. A uniform bank of width 4 metres is built all around the outside of the pond. Inside the pond, a rectangular platform of length 15 metres and breadth 10 metres is constructed. We will modify this problem to make it more complicated: **New Problem:** A rectangular pond has a length of 75 metres and a breadth of 50 metres. A uniform bank of width 6 metres is built all around the outside of the pond. Inside the pond, two rectangular platforms are constructed: one with length 15 metres and breadth 10 metres, and another with length 20 metres and breadth 12 metres. 1. Find the area of the bank. 2. Find the area of water in the pond excluding both platforms. 3. If grass is planted on the bank at a cost of 30 per square metre, find the total cost of grassing the bank. --- 2. **Formulas and Important Rules:** - Area of rectangle = length × breadth - The bank surrounds the pond, so the outer rectangle including the bank has dimensions increased by twice the bank width. - The area of the bank = area of outer rectangle (pond + bank) - area of pond - The area of water excluding platforms = area of pond - sum of areas of platforms - Total cost = area of bank × cost per square metre --- 3. **Step-by-step Solution:** **Step 1: Calculate the dimensions of the outer rectangle including the bank** - Length including bank = $75 + 2 \times 6 = 75 + 12 = 87$ metres - Breadth including bank = $50 + 2 \times 6 = 50 + 12 = 62$ metres **Step 2: Calculate the area of the outer rectangle (pond + bank)** $$ \text{Area}_{outer} = 87 \times 62 = 5394 \text{ m}^2 $$ **Step 3: Calculate the area of the pond** $$ \text{Area}_{pond} = 75 \times 50 = 3750 \text{ m}^2 $$ **Step 4: Calculate the area of the bank** $$ \text{Area}_{bank} = \text{Area}_{outer} - \text{Area}_{pond} = 5394 - 3750 = 1644 \text{ m}^2 $$ **Step 5: Calculate the areas of the two platforms inside the pond** - Platform 1 area = $15 \times 10 = 150$ m$^2$ - Platform 2 area = $20 \times 12 = 240$ m$^2$ - Total platform area = $150 + 240 = 390$ m$^2$ **Step 6: Calculate the area of water in the pond excluding the platforms** $$ \text{Area}_{water} = \text{Area}_{pond} - \text{Total platform area} = 3750 - 390 = 3360 \text{ m}^2 $$ **Step 7: Calculate the total cost of grassing the bank** - Cost per square metre = 30 - Total cost = $1644 \times 30 = 49320$ --- **Final answers:** 1. Area of the bank = 1644 m$^2$ 2. Area of water excluding platforms = 3360 m$^2$ 3. Total cost of grassing the bank = 49320