Question:medium

The cost of fencing a rectangular plot is ₹ 200 per ft along one side, and ₹ 100 per ft along the three other sides. If the area of the rectangular plot is 60000 sq. ft, then the lowest possible cost of fencing all four sides, in INR, is

Updated On: Jan 15, 2026
  • 90000
  • 160000
  • 120000
  • 100000
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The Correct Option is C

Solution and Explanation

To determine the lowest cost for fencing a rectangular plot, consider both the perimeter for cost calculation and the area for the given condition.

Let the length be l and the breadth be b. The area is fixed at:
l×b=60000

The fencing cost varies by side. The costs are as follows:

  • One length side: ₹ 200 per foot
  • The other three sides (one length and two breadths): ₹ 100 per foot

The total fencing cost is calculated as:
Cost=200×l+100×(2×b+l)

This simplifies to:
Cost=200l+200b+100l=300l+200b

The objective is to minimize this cost subject to the constraint lb=60000.

From the area constraint:

b=60000l

Substitute this into the cost equation:
Cost=300l+200×(60000l)

Simplifying further:

Cost=300l+12000000l

To find the minimum cost, differentiate the cost with respect to l:

dCostdl=300−12000000l²

Setting the derivative to zero to find the minimum:

l³=40000

Solving for l yields l=200. Consequently, b=60000/200=300.

Substituting these values back, the minimal cost is computed as:

Cost=(300×200)+(200×300)=120000

Therefore, the minimum cost to fence all sides is ₹ 120000.

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