The breadth of a rectangular field is 60% of its length.\nIf the perimeter of the field is 800 m, what is the area of the field in sq m?

Introduction:
This question tests perimeter-to-area conversion when a proportional relationship between breadth and length is given. If breadth is 60% of length, we can write breadth as 0.6 times length. The perimeter gives an equation involving length and breadth. Solving that equation provides the actual dimensions, and then area is computed as length * breadth. This is a standard aptitude problem that checks whether you correctly convert a percentage relationship into an algebraic equation and avoid common mistakes like treating 60% as 60 metres or confusing perimeter with area.

Given Data / Assumptions:

• Perimeter P = 800 m
• Breadth B = 60% of length L => B = 0.60L
• Perimeter formula: P = 2(L + B)
• Area formula: A = L * B

Concept / Approach:
Use perimeter to find L + B. Substitute B = 0.6L to solve for L. Then compute B, and finally compute area. This is a multi-step but straightforward algebraic substitution problem.

Step-by-Step Solution:
2(L + B) = 800 => L + B = 400B = 0.60LSo L + 0.60L = 4001.60L = 400 => L = 400 / 1.60 = 250B = 0.60 * 250 = 150Area = L * B = 250 * 150 = 37500

Verification / Alternative Check:
Check perimeter: 2(250 + 150) = 2*400 = 800 m, matches. Also breadth is 150, which is 60% of 250, matches. Therefore area must be 250*150 = 37500 sq m. The value is also reasonable for a field with sides 250 m and 150 m.

Why Other Options Are Wrong:
47500, 57500, 77500: come from incorrect length calculation or wrong multiplication.35000: typically due to rounding or using 0.6 on the wrong dimension.

Common Pitfalls:
Forgetting perimeter is 2(L + B).Treating 60% as 60 instead of 0.60.Mixing up which dimension is 60% of the other.Computing area using perimeter values directly.

Final Answer:
37500 sq m