CAT 2021 Question Paper | Quant Slot 3

CAT 2021 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 19 : 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

Video Explanation

Explanatory Answer

Let the length be x and the breadth be y,
Then the area of the region will be
x×y = 60000
Then the cost of fencing the region will be
200x + 100x + 100y + 100y
300x + 200y

Now we know that the Arithmetic mean ≥ Geometric mean.
So,
\( \frac { 300 x + 200 y } { 2 } \)≥ \( \sqrt [ 2 ] { 300 x \times 200 y } \)
300x + 200y ≥ 2 \( \sqrt [ 2 ] { 300 x \times 200 y } \)
300x + 200y ≥ 2 \( \sqrt [ 2 ] { 300 \times 200 \times x y } \)
300x + 200y ≥ 2 \( \sqrt [ 2 ] { 300 \times 200 \times 60000 } \)
300x + 200y ≥ 2 \( \sqrt [ 2 ] { 60000 \times 60000 } \)
300x + 200y ≥ 2 (60000)
300x + 200y ≥ 120000)
So we can say the cost will always be greater than 120000

The answer is '120000'

Choice C is the correct answer.