Painting a rectangular boundary: The length and breadth of a rectangular field are in the ratio 8:7. If painting the boundary (perimeter) costs Rs 3000 at Rs 10 per metre, find the area of the field in square metres.

Introduction / Context:
Cost-per-metre on a boundary gives perimeter. With side ratio known, we can solve dimensions and compute area.

Given Data / Assumptions:

• Length : Breadth = 8 : 7
• Total cost = Rs 3000 at Rs 10 per m → Perimeter P = 3000 / 10 = 300 m

Concept / Approach:
Let L = 8k, B = 7k. Then perimeter P = 2(L + B) = 2 * (15k) = 30k. Solve k from P, then area L*B.

Step-by-Step Solution:

Verification / Alternative check:
Perimeter check: 2*(80+70) = 300 m equals the derived perimeter from cost; consistent.

Why Other Options Are Wrong:
1400, 4400, 3600, 4900 do not match the product 80*70 under the given perimeter constraint.

Common Pitfalls:
Using 8:7 as difference instead of ratio or forgetting to double the sum when computing perimeter.

Final Answer:
5600 sq.m