NinetynineCAT 2021 Slot 3 QA Q19 Inequalities & Modulus
Question 19 of the Quantitative Ability (QA) section, CAT 2021 Slot 3, with CAT's official answer and a worked solution.
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
- A90000
- B160000
- C120000
- D100000
Answer: (C) 120000 Inequalities & Modulus MCQ
Solution
- Let the costly side be \(a\) and the other side \(b\), \(ab = 60000\).
- Cost \(= 200a + 100a + 100b + 100b = 300a + 200b\).
- By AM-GM, \(300a + 200b \ge 2\sqrt{300 \cdot 200 \cdot 60000} = 2 \times 60000 = 120000\), with equality at \(a = 200, b = 300\).