The cost of levelling a circular field at 50 paise per square metre is Rs 7700. Using π = 22/7, what will be the cost (in rupees) of putting up a fence all around the field at Rs 1.20 per metre?

Introduction:
This question combines area, circumference and unit cost concepts. The cost of levelling the field gives you its area, from which you can determine the radius of the circular field. Once the radius is known, you can compute the circumference and then calculate the cost of fencing based on a cost per metre.

Given Data / Assumptions:

• Levelling cost = 50 paise per square metre = Rs 0.50 per m².
• Total levelling cost = Rs 7700.
• The field is circular.
• Use π = 22/7.
• Fencing cost = Rs 1.20 per metre.
• We need the total fencing cost in rupees.

Concept / Approach:
First, use the levelling cost to find the area of the circular field. Then use the area formula A = πr² to compute the radius. Once we have the radius, the circumference C = 2πr gives the length to be fenced. Multiplying the circumference by the fencing rate gives the required cost.

Step-by-Step Solution:
Step 1: Find the area of the field.Levelling cost per m² = Rs 0.50.Total cost = Rs 7700.Area = Total cost / rate = 7700 / 0.50 = 15400 m².Step 2: Use area of circle formula A = πr².15400 = (22/7) * r².Multiply both sides by 7/22:r² = 15400 * (7/22).Note that 15400 / 22 = 700, so r² = 700 * 7 = 4900.Hence r = √4900 = 70 m.Step 3: Find the circumference to be fenced.C = 2πr = 2 * (22/7) * 70.Simplify: (2 * 22 * 70) / 7 = (44 * 10) = 440 m.Step 4: Compute fencing cost.Cost = 440 m * Rs 1.20 per m = 440 * 1.2 = Rs 528.

Verification / Alternative check:
We can re-check by reversing: if the radius is 70 m, area with π = 22/7 is (22/7)*70² = (22/7)4900 = 22700 = 15400 m², matching the area derived from levelling cost. Circumference for radius 70 m is indeed 440 m. Multiplying 440 by 1.2 again gives Rs 528, confirming the result.

Why Other Options Are Wrong:
Rs 132 and Rs 264 correspond to smaller circumferences and would imply a smaller radius than calculated. Rs 1056 is double the correct value, which would arise from mistakenly doubling the circumference or the cost rate. Rs 352 does not match any consistent interpretation of the data. Only Rs 528 correctly follows from the area and circumference computations.

Common Pitfalls:
Students often make mistakes in unit conversion between paise and rupees, or forget that 50 paise equals Rs 0.50, not Rs 50. Others mis-handle the π = 22/7 fraction or do not simplify properly when solving for r². It is important to proceed step by step: find area, then radius, then circumference, then cost.

Final Answer:
The cost of putting a fence around the circular field is Rs 528.