CAT 2021 Set-3 | Quantitative Aptitude | Question: 11

Question

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

• A. $160000$
• B. $100000$
• C. $120000$
• D. $90000$

Answer 1

Let’s draw the diagram.

Let the length and breadth of the rectangle be $\text{L ft},$ and $\text{B ft}$ respectively.



Total cost $= 200\text{L} + 100\text{B} + 100\text{L} + 100\text{B} = 300\text{L} + 200\text{B} \quad \longrightarrow (1)$

Area of rectangle $= \text{L} \times \text{B} = 6000 \quad \longrightarrow (2)$

We know that, $\text{AM} \; \geq \text{GM}$

$\Rightarrow \frac{300\text{L} + 200\text{B}}{2} \geq \sqrt{300\text{L} \ast 200\text{B}}$

$\Rightarrow \frac{300\text{L} + 200\text{B}}{2} \geq \sqrt{6000 \times 60000}$

$\Rightarrow 300\text{L} + 200\text{B} \geq 2 \times 60000$

$\Rightarrow \text{Total Cost} \geq 120000$

$\therefore$ The lowest possible cost of fencing all four sides in INR is $120000.$

Correct Answer $:\text{C}$