The length and breadth of a rectangular field are in the ratio 8 : 7.\nThe boundary of the field is painted at a cost of ₹10 per metre, and the total painting cost is ₹3000.\nFind the area of the rectangular field in sq m.

Introduction:
This problem combines perimeter (boundary length) with ratio-based dimensions. Since painting cost is given per metre for the boundary, the total cost directly gives the perimeter. Once perimeter is known and the ratio of length to breadth is given, we can find the actual dimensions by introducing a common multiplier. After computing the length and breadth, area is found by multiplying them. This is a typical aptitude “ratio + perimeter + area” question that checks multi-step reasoning and correct translation from cost to perimeter.

Given Data / Assumptions:

• Length : breadth = 8 : 7
• Painting cost per metre = ₹10
• Total painting cost = ₹3000
• Perimeter P = total boundary length
• Perimeter formula: P = 2(L + B)

Concept / Approach:
First compute perimeter: P = 3000/10. Then express L = 8k and B = 7k. Substitute into perimeter equation to solve for k. Finally compute area = L * B. This keeps the process clean and prevents guesswork.

Step-by-Step Solution:
Perimeter P = 3000 / 10 = 300 mSo 2(L + B) = 300 => L + B = 150Let L = 8k and B = 7kThen L + B = 15k = 150k = 10L = 8*10 = 80 m, B = 7*10 = 70 mArea = 80 * 70 = 5600 sq m

Verification / Alternative Check:
Check perimeter: 2(80 + 70) = 2*150 = 300 m, matches boundary length from cost. Painting cost then is 300*10 = ₹3000, consistent. With correct dimensions, area must be 5600 sq m. The magnitude also makes sense for an 80 m by 70 m field.

Why Other Options Are Wrong:
1400, 3600, 4400, 4800: these correspond to incorrect k values or mixing up perimeter with area. They do not match L + B = 150 along with 8:7 ratio.

Common Pitfalls:
Using total cost as perimeter directly without dividing by ₹10 per metre.Forgetting that ratio parts must sum to 15k.Using L - B instead of L + B from perimeter relation.Arithmetic errors in 80*70.

Final Answer:
5600 sq m